Motaz Agouri, an official at Benghazi security directorate's media office, said the explosion took place during Friday prayers inside the Saad Ibn Ibada mosque in Benghazi's busy Berka district.
A twin bombing attack in a mosque claimed the lives of two people and 55 other injured.
In January, two auto bombs exploded near Benghazi's largest mosque at intervals of 30 minutes, at a time when people were leaving after prayer. The devices appear to have been activated remotely using a mobile phone, one military source said.
In January, a twin vehicle bombing near a mosque in Benghazi's Salmani neighborhood killed at least 33 people.
No group immediately claimed responsibility for the attack.
"Direct or indiscriminate attacks against civilians are prohibited under global humanitarian law and constitute war crimes", UNSMIL said in a post on Twitter. The LNA has been battling Islamists, including some linked to Daesh and al-Qaeda.
"Turkey attaches importance for peace, security and stability to prevail in Libya and supports Libya's efforts against terrorist groups seeking to drive the country towards chaos", it added.
Haftar began his military campaign in response to continuous bombings and assassinations by on Islamist militants in Benghazi in May 2014.
Video showed Mahmoud al-Werfalli - who was already wanted by the International Criminal Court over 33 suspected extra-judicial killings - apparently shooting dead the detainees at the scene of the blasts.
The UN-backed unity government based in the capital has struggled to assert its authority outside western Libya.
Libya has been wracked by violence and divisions since dictator Moamer Kadhafi was toppled and killed in a 2011 NATO-backed uprising.