The explosions hit the mosque at the start of weekly prayers in Libya's second city, which lies 1,000 kilometres (620 miles) east of Tripoli, a security source told AFP.
One bomb was hidden in a coffin in the courtyard of the mosque and another in a shoe cabinet at the entrance, the source added.
At least one person was killed and 62 wounded, according to a spokeswoman for the city's Al-Jala hospital, Fadia al- Barghathi.
There was no claim of responsibility for that attack, which underscored the ongoing chaos in the Benghazi region which is controlled by the forces of military strongman Khalifa Haftar.
Haftar, who opposes a UN-backed unity government based in Tripoli, announced Benghazi's "liberation" from jihadists in July last year after a three-year campaign, but sporadic violence has continued.