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.
In the wake of the blasts debris was left scattered across the floor of the mosque, with windows blown out and bloodstains smeared on the wall.
The security source said one bomb had been hidden in a coffin in the courtyard of the mosque and another in a shoe cabinet at the entrance.
One person was killed and 149 wounded, according to Moataz Trabelsi, spokesman for the health ministry of the parallel administration based in the east of the North African country.
A previous hospital bulletin spoke of 62 wounded.
The blasts follow twin car bombings outside a mosque in Benghazi after prayers on January 24 that left nearly 40 people dead.
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 IS in July last year after a three-year campaign, but sporadic violence has continued.
The United Nations mission in Libya condemned the latest "brutal bombings" and said the reports of civilian casualties were "deeply concerning".
"This heinous act should not provide a justification for revenge attacks. Prompt, impartial investigations should bring perpetrators to justice," the mission said on Twitter.
Fears over potential reprisals are heightened by the reported summary execution of around 10 IS prisoners by a commander loyal to Haftar following last month's bombings.
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.
Werfalli on Tuesday said he had handed himself in to military police under Haftar's command, but it was not possible to confirm his arrest from an independent source.
Libya has been wracked by violence and divisions since dictator Moamer Kadhafi was toppled and killed in a 2011 NATO-backed uprising.
The UN-backed unity government based in the capital has struggled to assert its authority outside western Libya. Haftar supports the rival administration based in the east.
The UN is currently trying to negotiate an end to the current political turmoil by agreeing parliamentary and presidential elections later this year, but there is deep scepticism over whether they will take place.
On September 11, 2012, suspected militants linked to Al-Qaeda attacked the US consulate in Benghazi , killing ambassador Christopher Stevens and three other Americans.APP