Police spokesman Abu Bakr Abdel-Karim says the arrests yesterday and today were based on a forensics report which found that the detainee, Talaat Shabeeb, was beaten to death.
He says the policemen will be held for four days pending further investigations.
President Abdel-Fattah el-Sissi delivered a speech last week vowing to punish officers who make mistakes amid mounting criticism of the force following the death of three detainees in recent weeks.
Police brutality was one of the main grievances of protesters in the 2011 uprising that toppled longtime autocrat Hosni Mubarak.