According to media reports, the local mayor cited an electrical short circuit as a possible cause.
The 21 nuns present in the convent were brought to safety unharmed on Sunday night, with only one 87-year-old nun suffering from mild smoke inhalation.
According to the Ansa news agency, the nuns were watching the evening rosary prayer for peace with Pope Leo XIV in Rome on television when the fire broke out.
As a result, the fire spread through the wooden roof truss to the entire convent building, as drone videos released by the fire brigade show.
Firefighters are said to have managed to save some valuable sacred art treasures from the monastery, which was founded in the 17th century.
Carlo Acutis, who was canonised by Pope Leo XIV last month, received his First Communion at Bernaga Monastery in 1998.