They were accused of violating the rules of the audience of sports events and illegally wearing police uniforms.
They are also banned from participating in sports events for three years.
Pussy Riot said this was a protest against human rights violations in Russia. The thief dragged the four people out of the court.
The incident interrupted the second half of Croatia's match against the French team for about 25 seconds. The French team won 4-2.
Pussy Riot had previously held high-profile protests against President Vladimir Putin. In 2012, three members were imprisoned for anti-Putin punk songs at the Moscow Cathedral.
Three women and a man ran to the court, although one woman was attacking on the sidelines. They wore police uniforms: white shirts, black trousers and epaulettes.
A woman managed to pay tribute to the French star Kylian Mbappé and was taken away from the stadium.
But the male intruder was caught angrily by Croatian defender Dejan Lovren. After the incident, Lovren told reporters: "I just lost my head, I caught the person, I hope I can throw him away from the stadium."
The three women's World Cup invaders were named Nika Nikulshina, Olga Kurachyova and Olga Pakhtusova.
A statement by Pussy Riot stated that the purpose of the protest included the Russian authorities:
Release all political prisoners
Stop illegal arrest at public gatherings
Allow political competition in the country
Stop making criminal cases and remand people for no reason
The statement quoted a Russian poet, Dmitry Prigoff, who compared "the heavenly police who spoke to God on his walkie-talkie" with "the world who made criminal cases."
Russian anti-Putin activist and blogger Alexei Navalny posted a video clip on Twitter showing two pitch intruders being investigated.
Hearing an angry voice shouted at Mr. Verzilov and one of the women - their mock police uniforms looked messy.
"Sometimes I regret that this is not 1937," said the disengaged person, alluding to the terrorist activities of the communist era incited by the Soviet dictator Joseph Stalin.
Comments