The devices, placed inside bags, appear to have been activated remotely using a mobile phone, a military source said.
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.
One person was killed and 149 wounded, according to Moataz Trabelsi, spokesman for the health ministry of the parallel administration.
Twin vehicle bomb attacks hit a mosque in Benghazi's Salmani district two weeks ago, killing 34 people and injuring more than 100 others.
"This heinous act should not provide a justification for revenge attacks".
Jihadists and the forces of general Khalifa Haftar have been fighting to gain control of the city for over three years before Haftar announced that his troops has retaken it last July.
"Direct or indiscriminate attacks against civilians are prohibited under global humanitarian law and constitute war crimes", the mission added, calling for "prompt, impartial investigations to bring perpetrators to justice".
Libya has been wracked by violence and divisions since dictator Moamer Kadhafi was toppled and killed in a 2011 Nato-backed uprising.
Following last months bombing in Benghazi, video footage emerged of 10 blindfolded men being executed at the site of the attack. The western government has struggled to assert its authority across the country.
Mr al-Werfalli is wanted by the ICC for allegedly carrying out a number of similar killings.
The United Nations has been trying to mediate for years, hoping elections can help stabilize Libya.