Italian authorities have long complained about a lack of transparency from Cairo in the investigation.
The 28-year-old Italian, who was a student at Cambridge, had been researching trade unions, a politically sensitive subject in Egypt. His body was found on 3 February, a week after his disappearance in Cairo.
Two of the suspects detained are the wife and sister of the alleged gang leader. They had been arrested in the sister's apartment, where an official said police found a bag with Mr Regeni's passport and wallet.
The other two are the brother-in-law and brother of the head of the gang.
All four are accused of concealing a criminal and hiding stolen goods, officials said.
On Thursday, Egypt's interior ministry said police had found a bag belonging to the student during a raid on a flat linked to the gang. All its four members were said to had been killed in a shoot-out.
The group specialised in abducting foreigners while posing as policemen, it added.