Several countries, including England and Wales, as well as Poland, the Czech Republic, and Sweden, have indicated that they would not play Russia.
The World Cup 2022 play-offs are set to take place in March and will pit Russia against Poland before facing either the Czech Republic or Sweden if they win.
On Thursday, Russian President Vladimir Putin launched a military invasion of neighboring Ukraine.
Cezary Kulesza, president of the Polish Football Association, called Fifa's decision "absolutely reprehensible," while the Swedish Football Association and the Czech Football Association repeated their refusal to face Russia.
"We're not interested in playing this game of looks." Our position remains unchanged: No matter what the name of the team is, the Polish National Team will not play with Russia.
The Swedish Football Association's president, Karl-Erik Nilsson, informed Fotbollskanalen that they were "not satisfied" with Fifa's decision.
"Our opinion is not different today, and the situation in Ukraine has not altered merely because we received the communication from Fifa, so we have no alternative opinion today," he stated.
"We also want to talk to Poland and the Czech Republic so that we can tell Fifa what we think, but we anticipated Fifa to take a tougher approach." We would have done the same."
Sweden, together with the Netherlands and Switzerland, are in the same group as Russia for the women's European Championship, which takes place in England in July.
Fifa stated that discussions will take place with other sporting organizations to determine whether Russia should be barred from participating in competitions.
"Fifa would like to underline its disapproval of Russia's use of force in its invasion of Ukraine," the international football's governing body said in a statement issued on Sunday.
"Violence is never a solution, and Fifa sends its sincere sympathies to all those impacted by the events in Ukraine.
"Fifa will continue its ongoing discussions with the International Olympic Committee, Uefa, and other sport organizations to determine any additional measures or sanctions, including potential exclusion from competitions, that will be implemented in the near future if the situation does not improve quickly.
"Fifa's thoughts are with everyone who has been affected by this startling and distressing circumstance."
The Football Association announced earlier on Sunday that England will not play any international matches against Russia at any level.
The FA stated that it "completely condemns the atrocities committed by the Russian government."
The governing body of English football has stated that the boycott will continue "for the foreseeable future."
The Football Association of Wales criticised Russia's invasion, saying it "stands in solidarity with Ukraine and feels an incredible amount of regret and astonishment at the country's recent developments."
Wales will also not "play any international contests against Russia in the foreseeable future, at any level of the game," according to the statement.
