The media report came after President Mubarak's ruling party won an overwhelming majority in elections which ended earlier this month and which monitors said were marred by widespread abuse.
"President Hosni Mubarak today asked Ahmed Nazif to form a new government," the short statement from MENA said on Tuesday.
Further statements from MENA said former Foreign Trade and Industry Minister Rachid Mohamed Rachid had been appointed to the new role of Trade and Industry Minister, overseeing both foreign and domestic trade.
Finance Minister Youssef Boutros-Ghali would retain his post, while Education Minister Ahmed Gamal Eddin Moussa had also kept his position, MENA reported.
A reshuffle is routine after parliamentary elections.
The prime minister's focus traditionally has been managing the economy, and senior officials do not expect changes at the investment ministry, which along with the finance and trade ministries make up the core group of economic reformists.
Other portfolios such as foreign affairs, defence and interior are widely viewed as being areas Mubarak directly controls, even if they officially answer to the prime minister.
Nazif is expected to announce changes in the health, labour, social security, housing and transport ministries on Wednesday, MENA said.