Inmates said there were no basic living conditions in the facility, including no heat or water.
The Interior Ministry sent its elite forces to the scene. Ambulances and fire-fighting vehicles were also reportedly there.
Deputy Justice Minister Givi Mikanadze told reporters the riot was caused by "certain figures" who rejected prison reform plans.
Mikanadze also said the situation was "under control."
Some 800 prisoners were expected to be transferred to the new building. Last night's transfer involved the first 100 of them.