The quartet were accused of contravening the rules for spectators at sporting events and wearing police uniforms illegally. They were also banned from attending sports events for three years.
Pussy Riot said its action was a protest against human rights abuses in Russia. The incident came during the second half of the Croatia v France final, which the latter went on to win 4-2.
The group has a history of high-profile protests against Russian President Vladimir Putin. Three of its members were jailed in 2012 for an anti-Putin song performed in a Moscow cathedral.
The group detailed the sentences and their prison conditions in a series of tweets.