"A group attempted to hold an illegal protest rally on Kaluzhskaya Square. Around 35 people were arrested," he said.
Four underage protestors have been released on the condition that they later report to court, the spokesman added. The others will stand trial today.
The spokesman also commented that the group had not professed allegiance to any party or organization.
The protest came as 30,000 people took part in May Day rallies in downtown Moscow.
May 1 is Spring and Labor Day across Russia, a national holiday. In Soviet times, May 1 saw massive pro-Communist Party rallies.
Russia's modern political parties have also taken the opportunity to hold rallies, with supporters of the ruling United Russia party, the Communist Party, the ultranationalist LDPR party and A Just Russia taking part in rallies across the city.
An opposition 'March of Dissent' also took place in St. Petersburg with the participation of some 350 demonstrators. No arrests were reported, although there are unconfirmed reports that two bags filled with excrement were thrown at Eduard Limonov, the leader of the banned National Bolshevik Party.