Friday’s demonstration “initially began peacefully” before escalating into “acts of vandalism”, state-run newspaper Invasor said.
“A smaller group of people stoned the entrance to the building and started a fire in the street with furniture from the reception area.”
Other state-run facilities, including a pharmacy and a government-operated market were also targeted, it added.
Footage circulating on social media appears to show rocks being hurled through the windows as people shout “liberty” and a large fire burns in the centre of the street.
Minint said in a statement that “specialised forces” were investigating the “acts of vandalism”.
Public dissent is uncommon in Cuba. While its 2019 constitution grants citizens the right to demonstrate, a law defining the extent of that right is currently stalled in the legislature.
Following rolling power cuts across the country in recent weeks, some Cubans have taken to protesting by banging pots and pans in the streets at night or at home.
The capital, Havana, which has seen blackouts of up to 15 hours a day, has been the epicentre of recent protests.
Last week, a group of students gathered at the University of Havana to protest disruptions to their education caused by the deepening energy crisis.