An Interior Ministry statement said that Manfred Schmidt had made the decision "for personal reasons".
Interior Minister Thomas de Maizière said that in Schmidt, the BAMF was losing a leader who had done "outstanding work".
But the BAMF has come under criticism from across the political spectrum in recent months for its slowness in processing asylum applications.
The Nuremberg-based authority has a backlog of around 250,000 applications.
"The dramatically increased numbers of asylum seekers in Germany have set a huge challenge for the BAMF as well as for states and local authorities," the statement read.
Schmidt had been president of the BAMF since 2010 and "has always acted in a level-headed and prudent way", it continued.
So far there is no news of a successor to Schmidt at the head of the BAMF.
Refugee entries rise sharply