The army chief announced the move in a TV address. The head of the constitutional court is expected to be sworn in as interim leader on Thursday.
Mr Morsi’s supporters denounced the move as a military coup and said he was being held in detention.
His opponents celebrated through the night in Cairo’s Tahrir Square.
But officials from Mr Morsi’s Muslim Brotherhood said its main rally in Cairo had come under attack by armed assailants and there were reports of deadly clashes elsewhere.
US President Barack Obama said he was “deeply concerned” by the latest turn of events and called for a swift return to civilian rule.
The military moved quickly after the TV address by army chief Gen Abdul Fattah al-Sisi, who said Mr Morsi, Egypt’s first freely elected president, had “failed to meet the demands of the Egyptian people”.
Military vehicles were seen fanning out across the capital.
Muslim Brotherhood media spokesman Gehad el-Haddad told the BBC that Mr Morsi had been put under house arrest and the “entire presidential team” was in detention.
Mr Haddad’s father, senior Morsi aide Essam el-Haddad, and Saad al-Katatni, head of the Brotherhood’s political wing, were among those held.
State-run al-Ahram newspaper reported that arrest warrants had been issued for 300 leaders and members of the Muslim Brotherhood.
TV stations belonging to the Brotherhood went off air at the end of Gen Sisi’s speech and state news agency Mena said managers at the movement’s Misr25 channel had been arrested.
Mr Haddad said a crowd of some 2,000 Morsi supporters had been shot at by men in civilian dress with machine guns at the main Brotherhood rally.
A notice on Mr Morsi’s Facebook page denounced the army for its “military coup”.
The statement asked Egyptian citizens – both civilians and military – to “abide by the constitution and the law and not to respond to this coup”.
But a number of clashes were reported in several Egyptian cities. At least 10 people were said to have been killed in the coastal cities of Alexandria and Marsa Matrouh, as well as in the southern city of Minya.
In Tahrir Square, thousands of anti-Morsi protesters celebrated with fireworks and honking car horns.
One protester, Omar Sherif, told Agence France-Presse: “It’s a new historical moment. We got rid of Morsi and the Muslim Brotherhood.”
The BBC’s Kevin Connolly in Cairo says no-one knows what will happen next. The danger, he says, is that both sides will try to settle differences by bringing supporters on to the streets.
The army has said it will not allow that to happen but, our correspondent says, it will not be easy to stop.
pvt
July 4, 2013 at 12:27 pm
There is no justification at all for the Egyptians to treat their democratically elected President the way they did. They keep calling it a revolution, but it is far from that. What is happening in Egypt is a dangerous ploy by people with hidden interests to destabilize the country and stagnate development. Egyptians should have given Morsi a chance to perform!
Summer K
July 4, 2013 at 1:42 pm
We should do the same to Sata and his evil cartel which is led by some satanic newspapEr editor
Chamachakomboka yafffffeeeeee
July 4, 2013 at 3:27 pm
Zambians should not resort to such point but resolve issues peacefully.
GUMU GUMU
July 4, 2013 at 3:31 pm
To those advocating for a coup in Zambia, do you really understand the conseqencies? Lets not take this peace for granted.
Shi mine
July 4, 2013 at 3:38 pm
Be thankful that peace prevails in zambia otherwise its not a good thing to wish for ZAMBIA .
FuManchu
July 4, 2013 at 3:57 pm
Peace should not be taken for granted as leadership has its perils when peoples expectations are not met. There is a lot that leaders can learn from what is happening in Egypt as the so called “democratically elected” is not a promise to peace.
CHRISTIAN
July 4, 2013 at 4:28 pm
Only a s.t.u.p.i.d i.d.i.o.t would advocate for such a s.t.u.p.i.d. thing. Those North Africans are destined to fight because they started those wars in biblical times. So here even if you pay me, I would not participate. Only power-hungry tongas and their followers would resort to such ancient deeds. Fusekeni ba kolwe imwe. It should sink in the minds of cow herders that their role on earth is to lead cows and embalming them whereas some tribes are born to lead people.
GREG
July 4, 2013 at 4:30 pm
Sammer K ulitole sana!
Villager
July 4, 2013 at 5:08 pm
I am shocked that a zambian can actually suggest to removed the president by force. That utter nonsense because one needs to listen to and watch news of what is happening around the world and see how how many untold sufferings and killings that follow such actions. Summer whoever you are must be backward. It is your parents and your relatives that will be killed if any such a thing was to happen. Mr. Sata is still your president whether you like him or not. There is only Zambia for all of us and once you cross the border, you become a refugee… cant you see you hater of HE. Do that to your grandpa in your village and stop suggesting foolishness. Bullshit…
BK
July 4, 2013 at 7:28 pm
Ba summer K muli batutu.What has happened in Egpty is a different situation to our Zambian type.Its the greed ego between Mislim and Christian there.Zambia will remain peaceful forever.People in this nation are higly cultured and have regard for others .Zambia is a christian nation and who so ever planted that idealogy planted peace.You are only a few blinds who are prophets of doom otherwise a good number of the citizens are currently satisfied with the leadership in place.Some of you you want manner to fall from heaven just work hard.USA is a great nation because it is a united thing incooperating 50 States and a district infact from coast to coast.Whilest others are uniting you are busy dividing.You and your greedness.
Tondo wabula Nsafu but ukupulukuta cimo Naba Nsafu
July 4, 2013 at 7:37 pm
Sammer K ulinama yampanga nangu ukamyange HH pamputi ifyo ulelanda teti fichitike.pumbafu!!!!!
BK
July 4, 2013 at 7:39 pm
Protest is determined by the number of people agrieved if you are the minority that cannot happen .Mwanawasa and Sata revamped the economy and currently a good number are enjoying the gains and cannot follow you,****** Summer.
ba nel
July 4, 2013 at 7:53 pm
@Christian your insult on tongas is not good at all. Your sentiments can grow and the coming generations may want to settle scores. Do not put in danger the peace being enjoyed for a long time by suggesting there is a more important ethinic grouping. Lozis are fighting for their own nation because of that kind of reasoning.
Air Mukwai_
July 5, 2013 at 3:40 am
Hamas should be also dismantled
the master
July 5, 2013 at 6:08 am
sad to those dead, may they rest in peace. “ati umwana ashenda atasha nina ukunaya”
they thought the westerns idea of removing mubarack and introducing democracy would work for them would work for them..now they look like fools
BK
July 5, 2013 at 3:00 pm
Tongas are exceptionally good citizens and as a Bemba I ADORE them.They are natuarally peaceful people and have greatly contributed to the peace that envelope Zambia.They are resolute,hardworking,less talkertive,accademic brains ,cultural rocksteads and backbone of Zambin.Insulting them by a Zambian amounts to insulting the national flag.They resemble a family firstbone ,of late Tongas and Bembas are now cousins.Ba Nel keep it up.
BK
July 5, 2013 at 3:20 pm
When you form a party like lets say ‘Christian Brotherhood party ‘just know that there is already a division short of inclusiveness.Now they look like fools with no direction .A theater of political rigor.Democracy is expensive because the elements that cements a coherent and consistent solidity of the same are rigorous and calls for a tolerant society that understands its tenecity and cultural sedimentally that has been laid with history.