The explosion, thought to have been caused by a gas leak, took place in a three-storey court bailiffs' office building at around 10:00 a.m. time (07:00 GMT).
"Preliminary reports indicate that the blast occurred in the basement," a spokesman for the ministry said.
A spokesman for the Emergency Situations Ministry in Ingushetia said 21 people had been rescued from the building. He added that four people had critical injuries and were in intensive care.
The Prosecutor General's Investigation Committee said on its website the blast may have been caused by a gas leak. It also denied reports that one person was killed in the explosion.
Other media reports said some people could be still trapped in the building.