Cheik Modibo Diarra was detained several hours earlier at his home in the capital Bamako on the orders of March coup leader Capt. Amadou Sanogo, the BBC reported.
Diarra had been due to travel to France Monday night, the BBC said.
"Our country is living through a period of crisis," Diarra said on television at 4 a.m. local time (11 p.m. Monday EST).
"Men and women who are worried about the future of our nation are hoping for peace," he said. "It's for this reason that I, Cheikh Modibo Diarra, am resigning along with my entire government on this day, Tuesday, Dec. 11, 2012. I apologize before the entire population of Mali."
Diarra was made prime minister of an interim government in April after the military officially handed power back to civilians. But tensions between the soldiers who led the coup and the civilian prime minister mounted in recent weeks.