The prison is located in the town of Al-Hawl in Hasakah's eastern suburbs, according to the Sana news agency.
The Kurdish Syrian Democratic Forces have launched a manhunt.
Earlier this month, the Syrian Arab News Agency has reported, citing local sources, that a major insurrection by Daesh prisoners had taken place at the al-Sinaa prison facility in the US-backed Syrian Democratic Forces-controlled area in Hasakah, northeast Syria.
The al-Sinaa prison contains Daesh fighters of various nationalities, and is run by the SDF under the supervision of US occupation forces, holding part of the estimated 10,000 ex-Daesh fighters that the SDF has in its custody. 20 percent of these 10,000 prisoners are said to consist of foreigners whose home countries have refused to repatriate them.
* Daesh (ISIL/ISIS/IS/Islamic State) is a terrorist organisation banned in Russia