The medical centre in Benghazi reported that "five bodies plus an indeterminate number of body parts" had arrived at the hospital, along with "more than 10 wounded people".
A military source said the car parked in front of the academy blew up as soldiers emerged from an awards ceremony for army promotions.
Benghazi, cradle of the 2011 uprising that toppled veteran Libyan dictator Muammar Gaddafi, has seen near-daily attacks on security and other targets in recent months as the weak central government struggles to rein in former rebel brigades turned militias.
On December 22, a suicide car bombing targeting a security post 50 kilometres from Benghazi left 13 dead.
Militants have also attacked foreign missions in Benghazi, including a September 2012 assault on the US consulate in the Mediterranean city that killed the ambassador and three other Americans.
On March 2, gunmen shot dead a French engineer in Benghazi.
Eastern Libya has become a bastion of Islamist extremists, with authorities avoiding a full-blown confrontation with heavily armed former rebels pending the formation of a regular army and police force.
