He also said a constitutional declaration aimed at curbing presidential powers had been cancelled.
Mr Mursi, who was elected in June, is a member of the Muslim Brotherhood.
Relations between the Brotherhood and the military have been tense since the fall of President Hosni Mubarak.
It is not clear whether the president has the power to sack the head of the armed forces, or whether Field Marshal Hussein Tantawi will accept the moves.
The BBC’s Yolande Knell in Cairo says the president’s intervention is clearly an attempt to take decisive action in his tug of war for control with the armed forces.
Under an interim constitutional declaration issued before Mr Mursi was sworn in, the president cannot rule on matters related to the military – including appointing its leaders.
The Supreme Council of the Armed Forces (Scaf), which issued the declaration, also dissolved the Egyptian Parliament, which is dominated by the president’s Islamist allies.
As head of the Scaf, Field Marshal Tantawi became Egypt’s interim ruler after President Mubarak was ousted following mass protests in February last year.
Sunday’s presidential announcement also said armed forces chief of staff Sami Annan was retiring.