Fahim is the former leader of the Northern Alliance, the group that helped US-led forces topple the Taliban government in late 2001.
With less than a month until Aug 20 presidential elections, Taliban militants have intensified their attacks throughout Afghanistan.
On Saturday, seven Taliban fighters, wearing suicide-bomb vests and carrying automatic weapons, attacked several government buildings in the eastern city of Khost as Ramazan Bashardost, one of 41 presidential candidates, was campaigning in the city.
Bashardost was not hurt in the attack, but three policemen and 14 civilians were wounded. The attackers were all killed by Afghan security forces.