Footage posted to social media appeared to show numerous fans taunt traveling supporters using derogatory slurs and terms relating to the Pakistani community during the Championship side’s dramatic late 3-2 win over their Premier League visitors at The Den.
The FA has now stated that they have knowledge of the incident and are planning to look into the matter.
A spokesperson said: “The FA can confirm that we are aware of a video posted on social media after the FA Cup match between Millwall and Everton.
“Discriminatory behaviour and chanting has no place in football and we will be investigating the matter.”
Millwall themselves also condemned the actions of their supporters, describing them as “abhorrent” and vowing to issue life bans for anyone found to be involved.
A club statement read: “Millwall Football Club is aware of, and extremely disappointed by, a video circulating online displaying alleged racist chanting during Saturday's victory over Everton.
"The club will, as is commonplace following such incidents, work with all relevant authorities during investigations into the matter and look to identify individuals involved. Anyone identified and guilty of such abuse will be banned from The Den for life.
"The club would like to place on record its gratitude to, and pride in, the vast majority of its supporters who gave their team outstanding backing throughout the match and who deserve to enjoy a memorable victory.
"They should be able to do so without being tarnished by behaviour they would find abhorrent.
"Millwall Football Club has a long and proud record of anti-discrimination work and on top of this investigation will continue to work tirelessly, alongside the authorities, to eradicate all forms from the game."
Before the match, a fracas between rival supporters led to one man being left with a slash wound to his face ahead of kick-off.
Millwall's victory came via Murray Wallace's late strike, which followed a controversial leveller from Jake Cooper, who had seemingly directed the ball into the net with his arm.
They progress through to the fifth round as a result of their win.