The women are the wife and a sister of one of four slain gang members whom police have linked to the brutal murder of Regeni, whose mutilated body was found more than week after his disappearance in Cairo on January 25.
They are accused of concealing a crime and being in the possession of stolen material, the official said.
Egyptian police announced on Thursday that they killed four gang members in a shootout, and then discovered Regeni's passport and wallet in the home of a suspect's sister.
"Italy insists: we want the truth," wrote Italian Foreign Minister Paolo Gentiloni on his Twitter, while prosecutors in Rome rejected the latest conclusions of the Egyptian probe.
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Italian media and western diplomatic sources in Cairo have voiced suspicions that Egyptian security services kidnapped and tortured to death the 28-year-old Cambridge University graduate student.
Rome prosecutor Giuseppe Pignatone said in a statement that "details communicated so far are not satisfactory to shed light on the death of Giulio Regeni. Investigations must therefore continue."
Quoted by Italian press, Regeni's parents said they were "injured and bitter" at Egyptian authorities' latest attempt to explain their son's death.
Regeni had been researching labour movements in Egypt, a sensitive topic, and had written articles critical of the government under a pen name.
In a statement late yesterday, the Egyptian interior ministry said it was investigating the gang's links to Regeni's murder.
"The investigation apparatus is continuing, in coordination with the Italian security team, in its efforts to examine the gang's links, and the circumstances of the crimes and the areas in which they occurred," the ministry said.