The footage, which appeared on social media, captures two alleged Spurs fans jumping up and down singing after the quarter-final match.
They chant “we hate Millwall” and are noticed by many people in the crowd leaving the stadium, before two two men suddenly approach them.
Without warning one of the men throws a punch at the fan, and he drops to the ground in a heap as his friend immediately goes to check on him.
The purported Millwall fan then heads off into the crowd with the rest of the supporters.
Police channelled fans ahead of the game and pictures emerged of the force restraining scuffles, but no arrests were made prior to kick-off, according to the Metropolitan Police.
The Met Police told Mirror Sport that it is waiting for a post-match arrest update but said nothing out of the ordinary had at this point been flagged.
Tottenham dominated their League One opposition in the 2pm kick-off on Sunday, sticking six past them at White Hart Lane.
Harry Kane hobbled off with an ankle injury early into the tie, but his replacement Christian Eriksen broke the deadlock on 31 minutes.
Son Heung-min then grabbed two more before Dele Alli made it four and Vincent Janseen added a fifth with his first goal from open play in 30 appearances for Spurs.
Son completed his hat-trick in stoppage time as Tottenham cruised into the semi-finals.