Fahim, a leader of the Tajik ethnic minority, served as senior vice president to President Hamid Karzai, who is due to step down at elections next month as NATO combat forces pull out of Afghanistan after 13 years of fighting the Taliban.
Aged 56, Fahim was accused of being a ruthless strongman who maintained his own militia forces, but he also received American support as Afghanistan sought stability after the fall of the Taliban regime in 2001.
"The government of Afghanistan has called for a three-day national mourning, during which the national flag will be half-hoisted for his demise.