The video, broadcast as the logo was beamed onto Moscow's Bolshoi Theatre on Tuesday, included a map of host nation Russia, including Crimea.
The clip was commissioned by Russia's World Cup organizing committee from a "local creative agency" and has now been edited to remove the "short sequence in question," FIFA says.
Russia annexed the Crimean peninsula in March to fierce opposition from many Western governments. The Ukrainian government still claims Crimea as part of its territory.
The original video has been removed from FIFA's YouTube channel and replaced with an edited version excluding the two-second sequence in which the map of Russia was shown.
The film was part of a light show used to display the World Cup 2018 emblem on the Bolshoi Theatre after it was unveiled by Russian cosmonauts on national TV.
The video was shown at a time when FIFA and UEFA are jointly mediating deadlocked talks between the Russian and Ukrainian football authorities over the status of Crimea's clubs. UEFA ruled in August it would not recognize matches played by three Crimean clubs absorbed into the Russian league system.
The video angered some Ukrainian commentators. Markiyan Lubkivskiy, who directed Ukraine's preparations to host Euro 2012 and is now an adviser to the head of the Ukrainian security services, called for legal action in an online post and suggested the video could aid the cause of pro-Russian separatists in Ukraine.
"Lawyers, get ready," he wrote. "If we don't react toughly to things like this, then soon nothing will be left of us."
The Ukrainian Football Federation did not immediately respond to a request for comment.