Hazem el-Beblawi gave no clear reason for the decision as he made the announcement.
"Today the cabinet took a decision to offer its resignation to the president of the republic," he said.
Mr Beblawi was appointed last July after the army toppled president Mohamed Mursi following mass protests.
The government's shock resignation comes amid widespread strikes in the country.
Public transport workers and bin collectors are picketing and there have been media reports of shortages in cooking gas.
The resignations have been offered to interim president Adly Mansour.
Fresh presidential elections will be held in Egypt in April, with defence minister and army chief Abdel Fattah al-Sisi widely tipped to win.
Field Marshal Sisi reportedly attended the meeting which preceded Monday’s announcement – and the move could be designed to pave the way for his presidential campaign.