The Interior Ministry statement, carried by state TV, said the shelling of the prison area killed 10 and wounded 40.
It did not say if the dead and wounded included prisoners from the jail known as Adra Prison, just northeast of Damascus. The statement did not say which specific insurgent group was responsible for the attack.
Later today, insurgents fired shells into residential neighborhoods in Damascus killing one person and wounding seven, according to state TV.
Today's shelling of Adra Prison and nearby areas came a day after government airstrikes on a Damascus suburb killed more than 20 people and wounded dozens in the latest wave of government attacks on the crowded rebel-held area.
The state news agency SANA also said today that government air force attacks killed more than 50 militants in the coastal province of Latakia, a stronghold of President Bashar Assad.
Syria's civil war, now in its fifth year, has killed more than 250,000 people and wounded more than a million according to the UN.