The protest occurred during a break in a regular session at the assembly, General National Congress spokesman Omar Hmaiden said.
There were no immediate reports of casualties, but Hmaiden said furniture had been smashed and some documents belonging to assembly members were missing.
The protesters were demanding that a constitution now being drafted should make Berber an official language on a par with Arabic.
Violence and lawlessness, much of it involving former rebel groups, has plagued the North African oil producer since the war that toppled Muammar Gaddafi in 2011.
The indigenous people of North Africa, known to others as Berbers and among themselves as Amazigh, were brutally suppressed under Gaddafi, who considered the teaching of their language and culture to be a challenge to Arab dominance.
They were among the mainstays of the rebellion, with their stronghold in the Nafusa Mountains southwest of Tripoli emerging as one of the main fronts.
Berber was the main language of North Africa before Arabic arrived with the Muslim conquest in the 7th century. It is still spoken in the Sahara and in mountainous parts of Algeria, Morocco and Tunisia as well as Libya.
(Reporting by Feras Bosalum; writing by Sami Aboudi in Dubai; Editing by Kevin Liffey)
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