The move by Prime Minister Ismail Sharif is in line with the political tradition that the government should resign at the start of a new presidential term.
Sisi was sworn in for his second, four-year term, as president three days ago.
He has the right to use the premier’s resignation as an opportunity to reshuffle the cabinet.
Ismail, 62, has been serving as prime minister since September 2015.
Prior to his appointment as prime minister, Sherif was the Minister of Petroleum and Mineral Resources from 2013 to 2015.
He previously travelled to Germany in November 2017 for health reasons, the source of which was never officially disclosed. Ismail returned to Egypt in January of this year.
His resignation was also confirmed by the spokesman of the presidency office, Bassam Radi.
Sisi and Sherif are known to enjoy a close working relationship, and the general-turned-president has publicly praised his prime minister on many occasions.