The mosque, one of the oldest in North Africa, is in the city of Aujla, 400 kilometers south of Benghazi.
No one is reported to have been injured in the collapse of the minaret.
Libyan archeological sites officials have dispatched a team of experts to the area analyze the extent of the damage and work out a plan to restore the mosque.
Built in 474 Hijri (1082), it is one of the main historic buildings remaining from the era of Fatimid rule in North Africa.
It has been repaired several times since then.
The mosque has a unique architecture, with bricks and wood used to build it.
A minaret is a tower in mosques across the Muslim world from where muezzins call Muslims to prayers.