The mostly jihadist rebel forces launched an attack on the regime-controlled prison last night, in the heaviest fighting for the jail in months, said the Syrian Observatory for Human Rights.
The military responded to the assault by firing a barrage of shells in the area around the prison.
After midnight, "the intensity of the fighting decreased between the army and members of the Al-Qaeda-linked Al-Nusra Front and another Islamist faction Ahrar al-Sham," it said in a statement.
It added that the clashes did not reach the buildings holding thousands of prisoners, mostly common criminals but also Islamist militants.
The jail, located on the northern outskirts of Aleppo, the commercial capital of Syria before a bloody uprising erupted in March 2011, has been besieged by rebels since April.
The Observatory denounced the "alarming" health conditions at the prison, including reported cases of tuberculosis and scabies.