"Al-Gamaa Al-Islamiya in Assiut will take over responsibility for the security of the city after hundreds of policemen went on strike and closed the police stations," the group said in a Friday statement.
The announcement was made at the group's headquarters in Assiut.
Police personnel began a strike on Friday in the city's five police stations to demand the resignation of Egypt's interior minister.
Assem Abdel-Maged, a senior member of Al-Gamaa Al-Islamiya, said the ultra-conservative Islamist group would not allow the city to remain in a security vacuum.
Abdel-Maged added that the group had begun setting up "security militias" tasked with securing public and private property in the city, especially banks.
He added that Al-Gamaa Al-Islamiya would secure all areas that had been abandoned by police. He also said that the group might coordinate its movements with Egypt's interior ministry.
"Any policeman who wants to leave his position can do so. But he will not be allowed to come back," Abdel-Maged said. "We want to purge the ministry of such elements anyway."
However, a senior member of Assiut's security directorate told Al-Ahram's Arabic-language news website that the government would "not allow anyone but police" to keep the peace in the city.