This is the fifth fire incident in the city in the last three weeks.
The fire brigade got a call at 7.14 am about the blaze in the court building, located near the campus of the Mumbai University in the southern parts of the city, the official of the Brihanmumbai Municipal Corporation's (BMC) disaster management unit said.
The fire brigade personnel rushed to the spot and managed to douse the flames in the building, which has been accorded a heritage status.
The police and the fire brigade officials are yet to ascertain the cause of the blaze.
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According to a sessions court official, the judges presided over their respective courts as usual from 11 am.
On December 18, 12 persons were killed when a massive fire broke out at a snack shop in the Saki Naka-Kurla area here.
On December 29, 14 persons were killed in a fire at an upscale pub in the Kamala Mills compound.
In yet another incident on January 4, four persons, including two children, were killed and five others seriously injured after an upper floor of a residential building in suburban Marol caught fire.