Two others suspected of involvement in setting the blaze are in police custody. A decision of whether to hold the suspects on remand will be made on Friday by the Pirkanmaa District Court.
Police are continuing their investigations but have been reticent on details. So far, a motive has not been established.
The blaze that began at the pizzeria in Tampere's main thoroughfare early Monday killed three people and injured five.
Accident investigators said on Thursday that the explosive force of the fire caused a blast wave, which demolished a door leading to the corridor inside the building.