The Interior Ministry's spokesman appeared on television to announce that the military unit had been discovered, and named 12 people who he said were members, Reuters reported on Sunday.
He said the group had shot dead five policemen last month in the province of Beni Suef.
The Muslim Brotherhood has been branded a terrorist group by the government, and security forces have killed about 1,000 of its members in the streets.
The Muslim Brotherhood says it is against violence and Egyptian army chief Abdel Fattah al-Sisi has staged a coup and undermining democracy.
State television aired what it said was a confession by one the military wing's members. He recalled meeting a man who he said had offered to teach him and others how to use weapons.
Human rights groups accuse the army-backed government of widespread human rights abuses and stifling dissent.
On July 3, the head of Egypt’s army General Abdel Fattah al-Sisi announced that President Mohamed Morsi was no longer in power. Al-Sisi also dissolved the Egyptian constitution.
The Chief Justice of Egypt’s Supreme Constitutional Court, Adli Mansour, was sworn in as interim president on July 4.
Since then, Egypt has been the scene of rival rallies and clashes between thousands of the supporters and opponents of Morsi.
NTJ/SHI