Motaz Agouri, an official at Benghazi security directorate's media office, said the explosions occurred during Friday prayers inside the Saad Ibn Ibada mosque in Berka district of Benghazi.
The official added that the bombs were placed in separate rooms inside the mosque.
No group has so far claimed responsibility for the attack, the second to hit Benghazi in nearly two weeks.
At least 33 people were killed in twin car bombings outside a mosque in Benghazi's central neighborhood of al-Sleimani on January 23.
Benghazi is controlled by the forces of military strongman Khalifa Haftar, who opposes a UN-backed government based in Tripoli.
Benghazi has been relatively calm since Haftar announced the eastern city's "liberation" from militants in July last year after a three-year campaign. However, sporadic violence has continued.
Libya has been wracked by violence and divisions since dictator Muammar Gaddafi was toppled and killed in a 2011 NATO-backed military invasion. The country has been since split between rival governments and militias.