There has been shows of support for Ukraine at football matches since Russia launched their invasion of the country last Thursday
The world and European football governing bodies said they would be banned "until further notice".
It means the Russian men's team will not play their World Cup play-off matches next month and the women's team have been banned from this summer's Euro 2022 competition.
Spartak Moscow have also been kicked out of the Europa League and their last-16 opponents RB Leipzig will advance to the quarter-finals.
Uefa has also ended its sponsorship with Russian energy giant Gazprom.
"Football is fully united here and in full solidarity with all the people affected in Ukraine," Fifa and Uefa said in a joint statement.
"Both presidents hope that the situation in Ukraine will improve significantly and rapidly so that football can again be a vector for unity and peace amongst people."
Fifa and Uefa decided to take action after Russia, supported by Belarus, launched a military invasion of neighbouring Ukraine last Thursday.
The Russian men's team had been scheduled to face Poland in a World Cup play-off semi-final on 24 March.
Russian football's governing body, the RFU, said it "categorically disagreed" with the decision and would challenge it "in accordance with international sports law".
Fifa had previously ruled that Russia must complete their upcoming games in neutral territory, under the title Football Union of Russia, and without their flag and anthem.
However, the announcement drew criticism - and Scotland and the Republic of Ireland joined several other nations, including England, Northern Ireland and Wales, as well as Poland, the Czech Republic and Sweden, in refusing to play against Russia.
Russia are in Northern Ireland's European Under-21 Championship qualifying group and their meeting in March will be cancelled.
On Monday, Scottish FA president Rod Petrie wrote to his Ukrainian counterpart "to send a message of support, friendship and unity", with those two nations due to meet in their World Cup play-off semi-final on 24 March.
The 2022 Champions League final, originally due to be played in St Petersburg on 28 May, has been moved to Paris while numerous clubs have taken their own steps to disassociate themselves from Russia.
Manchester United has terminated its sponsorship deal with Russia's national airline Aeroflot while Bundesliga club Schalke has cancelled its partnership with main sponsor Gazprom, having last week removed the Russian energy company's logo from its shirts.
"I can't understand why it took them 24 hours to make this decision," said Jim Boyce, former Fifa vice-president and honorary life president of the Irish FA, speaking to BBC Radio Ulster.
"What is happening is absolutely deplorable. Quite honestly, every possible sanction that can be imposed on Russia at the minute has to be done. I applaud Fifa and I applaud Uefa for the decision that they have made today."
Speaking on Monday, Tottenham manager Antonio Conte said: "The whole world has to be compact and show [it is] solid against the stupidity of the people."
He added: "I think it's right to express our disappointment about the stupidity about some decisions. Football and Uefa has to be compact and to show to be strong."
The IOC says it is urging sport governing bodies to ban Russian and Belarusian athletes "in order to protect the integrity of global sports competitions and for the safety of all the participants", adding that "the current war in Ukraine puts the Olympic Movement in a dilemma".
It said there had been a "breach of the Olympic Truce" by those countries' governments.
"While athletes from Russia and Belarus would be able to continue to participate in sports events, many athletes from Ukraine are prevented from doing so because of the attack on their country," an IOC statement read.
The 2022 Winter Paralympics take place in Beijing from 4-13 March
The International Paralympic Committee is to meet on Wednesday to discuss Russia, with the Winter Paralympics set to start two days later.
The British Paralympic committee has called on Russians and Belarussians to be kicked out of the Games.
The British Olympic Association, along with the National Olympic Committee (NOC) of Germany, has demanded the immediate exclusion of Russia and Belarus from international sport.
The IOC said in their recommendations that wherever it was not possible to ban them from competing for organisational or legal reasons, such athletes should not compete under the name Russia or Belarus and should be classed as neutrals.
The Russian Olympic Committee has disagreed with the IOC, saying the decision "contradicts both the regulatory documents of the IOC and the [Olympic] Charter".
-- Courtesy of BBC Sport