Minister of State Christophe Mirmand told French broadcaster BFMTV the blast occurred around 9pm on Monday (5am AEST Tuesday) but would not confirm if the incident was an attack.
Media reports said an explosive device had detonated at the site.
Shortly before the explosion, a person was seen placing a backpack at the location before fleeing, BFMTV reported, citing Monaco security authorities and the regional newspaper Monaco-Matin. The suspect remains at large.
Images published by media outlets showed CCTV footage of a running man wearing a dark hat.
The building is located on a square near the border with France, and the suspect reportedly fled on foot towards the French town of Beausoleil.
According to Monaco-Matin, the three victims - a man, a woman aged between 50 and 60, and a teenager from the same family - were seriously injured.
Four other people suffered shock, Mirmand said. He added that an event of this kind had never occurred in the principality.
Eric Ciotti, the right-wing mayor of the nearby French city of Nice, around 20km away, described the incident as an "attack" in a post on X, calling it a "tragedy that strikes Monaco".
He expressed support for emergency services.
French rescue teams were deployed to support local responders, according to sources in the French Interior Ministry, and a joint police operation was launched to track down the suspect.
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