Two buildings were damaged in the blaze while nine prisoners and police were being treated for injuries, Fana reported. The remaining inmates have reportedly been moved to other facilities.
Many of the inmates at Qilinto were arrested in ongoing government crackdowns against months of protests in the central Oromo region and elsewhere.
According to the New York-based Human Rights Watch group, at least 500 people have been killed by security forces since the protests began in November.
Though demonstrations started among the Oromo, Ethiopia’s largest ethnic group, protests later spread to the Amhara, the country’s second most populous ethnic group.
Both groups say that a ruling coalition government is dominated by the Tigray ethnic group, which makes up about 6 percent of the population.
The government has denied that violence by the security forces is systemic, though a government spokesman told Al Jazeera recently that police officers “sometimes take the law into their own hands”, and pledging an independent investigation.
Authorities have blamed the unrest on opposition groups inside and outside of the country and what they have called “anti-peace” elements.