Mr Shafiq was appointed days before President Mubarak was forced out of office Egypt's Prime Minister Ahmed Shafiq has resigned, the country's ruling military council has announced in a statement.
A former transport minister, Essam Sharaf, has been asked to form a new government, the statement adds.
Mr Shafiq was appointed days before President Hosni Mubarak was forced out of office following days of anti-government protests.
Protesters saw Mr Shafiq as too closely associated to Mr Mubarak's rule, observers say.
"The Supreme Council of the Armed Forces decided to accept the resignation of Prime Minister Ahmed Shafiq and appointed Essam Sharaf to form the new government," the army said in a statement on its Facebook page.
Mr Shafiq was appointed by Mr Mubarak just days before he stepped down on 11 February after several weeks of popular protests against his rule.
It had been one of the protesters' key demands that Mr Shafiq and other top ministers appointed at the end of the Mubarak rule step down.
Analysis
President Mubarak may have gone, but the protests in Cairo have been continuing as people have been demanding the "old guard" of politicians step down. At the top of their list was Prime Minister Ahmed Shafik.
As a result his resignation, announced by the Armed Forces Supreme Council on its website, has been broadly welcomed by opposition groups. But a big demonstration is still planned for Friday in Tahrir Square where hundreds of people have been camping out.
The appointment of Essam Sharaf as the new prime minister is designed to placate them.
He's a former transport minister who opposed Mr Mubarak's government after stepping down from the cabinet, and supported the revolution.
The response from those demanding more change has been mixed, with some saying all politicians who served under Mr Mubarak should go while others think the new administration should be allowed to get on with the job of constitutional reform and elections.
Mr Sharaf's appointment is significant as he spoke out in support of the revolution and took part in the street protests, says the BBC's Alastair Leithead in Cairo.
It is a major step towards appeasing the demonstrators who have continued to camp out in Tarihr Square, as Mr Sharaf was a vocal opponent of the Mubarak government since his resignation as a minister five years ago, our correspondent adds.
Travel banThe military council, which has been running the country since Mr Mubarak stepped down, has previously ordered the government to run the country's affairs for six months "or until the end of parliamentary and presidential elections" and is also examining constitutional reforms.
On Monday, Egypt issued a travel ban on ousted President Mubarak and his family.
Mr Mubarak is believed to be living in his villa in Sharm el-Sheikh, but in poor health, and has not been seen or heard of publicly since stepping down.
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