BBC News and Al-Arabiya network say Col.-Gen. Abdel Fattah al-Sisi acted to get rid of the generals ahead of a plan to form a new military council.
The reports say al-Sisi removed six members from the Supreme Council of the Armed Forces. However, those men will still remain as members of the armed forces.
Sisi was appointed only weeks ago by Egyptian President Mohammed Morsi, who had forced then-Defence Minister Field Marshal Hussein Tantawi and the armed forces chief of staff Sami Anan to step down. Both now serve as consultants to the government.
Both men had been key members of the military council, which had broad legislative and executive powers.
The council ran the country after the fall of President Hosni Mubarak in February 2011 and in July this year, officially handed over power to Morsi – the country’s first democratically elected president and also, its first civilian leader.
Since coming to office, Morsi has been clawing power away from the military elite, which has been in charge for decades.
The supreme council stripped the presidency of many of its key powers before it handed the office to Morsi.
As well, the ruling generals decreed constitutional amendments that gave them the power to legislate after the military dissolved parliament, as well as control over the national budget and the drafting of a new constitution.
Morsi restored to his office the powers taken from him, seizing back sole control of the constitution drafting process and his powers to issue laws.