The pitch invasion by members of the punk band early in the second half of the final was a brazen act in Moscow's Luzhniki stadium in front of Russian President Vladimir Putin and other high-ranking officials from around the world.
The judge also banned the four from attending sports events for three years.
The four were Veronika Nikulshina, Olga Pakhtusova, Olga Kurachyova and Pyotr Verzilov, the only male.
Kurachyova said their stunt, which held up the game only briefly, was meant to promote freedom of speech and condemn policies of FIFA, soccer's global governing body.
"It is a pity that we disrupted the sportsmen," Kurachyova told reporters on Monday.
"FIFA is involved in unfair games unfortunately. FIFA is a friend of heads of states who carry out repression, who violate human rights."
Verzilov said the performance was also meant to show how "the state, in the form of the police, intrudes into people's lives".
Three of Pussy Riot's original members were jailed in 2012 for staging a protest against Putin in a church and the group has since become a symbol of anti-Kremlin direct action.
Croatian defender Dejan Lovren, who pushed the male intruder aside on the pitch, told reporters the incident had interrupted the game at an important moment for his team.
The match, which France won 4-2, was watched from the stands by Putin and the French and Croatian presidents.
(Reporting by Gabrielle Tétrault-Farber; Writing by Christian Lowe and Vladimir Soldatkin; editing by Richard Balmforth)
