The association said on Twitter that the Super Eagles would take on the Cranes at the “Nest of Champions” stadium in Uyo, southeastern Nigeria, next Wednesday.
The former African champions, who failed to qualify for this year’s competition, had previously been slated to take on the South Americans until their withdrawal.
Bolivian FA president Carlos Chavez attributed their cancellation to “armed conflict and the tense political situation in Nigeria”.
Nigerians go to the polls to elect a new president and parliament three days after the match, with political violence expected and the military tackling Boko Haram militants in the northeast.
The NFF said they had requested compensation from Bolivia for their last-minute withdrawal.
Nigeria beat Uganda 1-0 in their last meeting in the southwestern city of Abeokuta in 2007. Both teams are using the match to prepare for the 2017 Africa Cup of Nations.
A second friendly with South Africa has been scheduled for March 29 in Nelspruit.