Egypt's public prosecutor said on Sunday that Nazif is suspected of illicit gains and graft.
Nazif, who acted as Mubarak's premier for more than five years, will be in custody for 15 days as part of an investigation into the squandering of public funds.
Sources say assets of several former officials and ministers have also been frozen over corruption and use of violence against the peaceful protesters.
Nazif's arrest was announced shortly after Egypt's public prosecutor summoned former President Hosni Mubarak and his sons for questioning.
The Mubarak family is facing allegations of corruption as well as violence against the protests that ended his rule. Mubarak has rejected the accusations as libel.
In an interview with the Saudi television Al-Arabiya for the first time since his ouster in February, Mubarak said he is prepared to aid any probe into his family's assets outside Egypt. He also threatened to sue his accusers.
This comes as Egyptians continue to protest against the ruling military council -- now in power -- at Cairo's Liberation Square.
Protesters defied threats by the country's military to use force to end the protests. The protesters barricaded the square with barbed wire and beams on Sunday.
Hundreds of Egyptians have remained in the historic square, calling for the resignation of the head of the ruling military council, Field Marshal Mohamed Hussein Tantawi.
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