The blasts took place during Friday prayers, residents said. The devices appear to have been activated remotely using a mobile phone, one military source said.
Two weeks ago, around 35 people were killed by a twin bombing at a mosque in the same city.
Benghazi, Libya's second-largest city, is controlled by the Libyan National Army (LNA), led by eastern-based commander Khalifa Haftar. The LNA was battling Islamists, including some linked to Islamic State and al Qaeda, as well as other opponents until late last year in the Mediterranean port city.
Haftar, a possible contender in national elections that could be held by the end of 2018, has built his reputation on delivering stability in Benghazi and beyond, promising to halt the chaos that developed after a NATO-backed uprising ended Muammar Gaddafi’s long rule nearly seven years ago.
Haftar launched his military campaign in Benghazi in May 2014, in response to a series of bombings and assassinations blamed on Islamist militants.
In past months there have been occasional, smaller scale bombings apparently targeting LNA allies or supporters.