A spokesman for the Faryab provincial government, Ahmad Jawad Dedar, said today that the breakout took place the previous night.
A fourth inmate who was also trying to escape was killed in a shootout with security forces.
Dedar says the fugitives are low-level Taliban operatives who were jailed for planting roadside bombs.
The four inmates launched their breakout during the nightly count of prisoners, throwing several grenades and shooting guards with at least one pistol.