The source, who spoke on condition of anonymity, said the move would open the door to the formation of "private militias" and raise the spectre of "civil war."
The military source supported his assertions by pointing to the reaction to the statement by Islamist groups, some of whom quickly announced plans to set up 'popular committees' to replace striking police officers.
"This policy crosses the state's red lines...the armed forces will not accept anything that threatens national security," he said.
"Egypt's armed forces don't stand on the side of any political faction, but that's not an excuse for certain groups to begin forming militias," he added.
The source went on to warn that such a step "could prompt the military to intervene."
In a Sunday statement, the prosecutor-general's office urged members of the public "to exercise the right afforded them by Article 37 of Egypt's criminal procedure law to arrest anyone found committing a crime and refer them to official personnel."
The statement came within the context of an ongoing strike by Egyptian police officers that began last Tuesday. Police personnel in several Egyptian governorates – including Cairo and Alexandria – have since joined the strike to demand the dismissal of the interior minister and a halt to what they see as their being used as pawns in the country's ongoing political stalemate.
Meanwhile, Al-Gamaa Al-Islamiya's Construction and Development Party announced plans this week to establish 'security committees' in several Upper Egyptian cities to replace police in the event that the strikes persist.