Ganga Yogi, the chief of Rajbiraj prison, told The Kathmandu Post that the fire started when prisoners from Block B staged an arson attack.
The security guards resorted to firing multiple rounds of tear gas shells to bring the situation under control, but some of the inmates managed to escape the prison.
The prison had 397 inmates at the time of the incident.
Meanwhile, security forces quelled an hour-long unrest at Birgunj prison in Parsa.
Inmates had attempted to escape by breaking a large hole in the southern wall of the facility, the newspaper reported.
Prison chief Khemraj Bhusal told the newspaper that four inmates sustained minor injuries during the incident.