Sustained gunfire could be heard coming from Qilinto prison, on the outskirts of the capital Addis Ababa, after the fire broke out, local media reported.
The government confirms “some” deaths, while local media report that at least 20 people had died in the incident.
There has been an unprecedented wave of protests in Ethiopia in recent months.
Photos posted on social media on Saturday showed plumes of smoke rising from the prison compound.
Reports that the fire was started deliberately as part of an attempted jailbreak have not been independently verified.
There have been numerous protests in the Oromia region by members of the country’s largest ethnic group since November 2015.
Many Oromo activists are being held at the Qilinto facility, according to pro-opposition media.
New York-based Human Rights Watch says that more than 400 people have been killed in clashes with the security forces in Oromia, although the government disputes this figure.
Ethiopian Prime Minister Hailemariam Desalegn has blamed “anti-peace forces” for the violence.