An internal investigation is underway after two cells at Risdon Prison were set alight on Wednesday night.
The Justice Department confirmed the fires were quickly extinguished by prison officers and nobody received any injuries.
Acting Director of Prisons David Jackson said several prisoners were relocated within the prison due to the damage caused to the cells.
A department spokesman said there was no risk to the community as a result of the incident.
The Tasmania Fire Service and emergency service workers attended the prison on Wednesday night.
Police officers attended the prison and remained at the scene to patrol the perimeter as a precaution.
Corrections Minister Elise Archer said the quick action and professionalism of prison officers meant serious injuries were avoided.
She said Tasmania Police had visited Risdon Prison again on Thursday morning.
"Those involved in the incident will face disciplinary action as well as potential charges from Tasmania Police," Ms Archer said.
"The safety and security of prison staff and prisoners is something that we take extremely seriously."
Community and Public Sector Union state general secretary Thirza White said prison officers turned up to work each day expecting danger.
"As it stands, there are no physical injuries which is good, but it's important to remember that it's an incredibly dangerous and stressful job with a high incidence of PTSD," she said.
"The impact of this isn't just about today, it's about the future weeks and months."
Ms White said overcrowding of prisoners and understaffing of prison officers increased the likelihood of adverse situations occurring, such as the two fires.