Four members of the anti-Kremlin group burst into the pitch at the Luzhniki stadium.
Two reached the middle of the pitch.
Putin watched in shirtsleeves as police swiftly rounded up the intruders and dragged them into detention.
They appeared to be dressed in suits and hats.
One of the protesters was reported to be well known Nadezhda Tolokonnikova, 28, jailed in 2012 for ‘hooliganism’ after an anti-Putin protest in a Moscow cathedral.
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Pussy Riot claimed responsibility for the stunt.
Among their demands were “to release all political prisoners” and “stop illegal arrests at rallies”.
They called for an end to fabricating criminal cases and jailing protesters.
The BBC commentator for the match between France and Croatia, said: “Oh, we’re going to have a stoppage now!
“I’m afraid, as you can see, time to focus on something else.
“First time it’s happened in the entire World Cup finals.
“Russian authorities have dealt with most things calmly with a smile.”
He added: “Not sure that might happen next.”
Shortly after the incident, the Pussy Riot protest group took to Twitter and released a statement about the pitch invasion.
They wrote: “NEWS FLASH! Just a few minutes ago four Pussy Riot members performed in the FIFA World Cup final match — ‘Policeman enters the Game’.”
“Today 11 years old as the great Russian poet Dmitry Alexandrovich Prigov died. Prigov created in Russian culture the image of militiamen, the host of heavenly statehood.
“The Heavenly Policeman, on the prigovu, is talking on the radio with his own God. Earth same fabricates criminal cases. While the sky policeman is gently watching the jerseys in the world cup, the earth policeman is preparing to rally rallies.
“The Heavenly policeman affectionately touches the flower in the field and rejoices in the win of the Russian National Team, and the earth’s policeman is neutral to Oleg Sentsov Heavenly policeman – towering as an example of statehood, earth policeman – makes everyone hurt.
“The Heavenly policeman protects the dream of a baby, the earth’s same policeman pursues political prisoners, planting for reposts and likes.
“The Heavenly policeman and there is the organiser of the beautiful carnival of the world cup, the earth policeman is afraid of The Heavenly policeman is caring for the observance of the rules of the game, the earth policeman enters the game without being considered with the rules.
“The World Cup reminded the possibility of heavenly militiamen in the beautiful Russia of the future, but every day entering the game without the rules of the earth policeman destroys our world.
“When the earth policeman enters the game we demand:
“1. Free all political prisoners.
“2. Don’t plant for likes.
“3. Stop illegal arrests at rallies.
“4. Allow political competition in the country.
“5. Don’t fabricate criminal cases and don’t keep people just like that in sizo.
“6. Turn the earth militiamen into the heavenly militiamen.”
France declared overall victory
(Additional reporting by Will Stewart.)