The Football Association is set to investigate claims that Millwall supporters aimed racially motivated abuse at Tottenham Hotspur’s South Korea forward, Son Heung-min, during the FA Cup quarter-final between the clubs at White Hart Lane.

Son was the star turn, scoring a hat-trick in Tottenham’s 6-0 win, on an afternoon when the club’s first-choice centre-forward, Harry Kane, limped off with an ankle injury that could end his season.

There were also reports of trouble involving supporters outside the stadium before and after the match. The Metropolitan Police confirmed two people were arrested and charged with public order act offences.

The FA is aware of the chants against Son, although it will wait for the report of the referee, Martin Atkinson, and observations from both clubs and the Met Police before it determines how to proceed.

Son was subjected to chants of “DVD” and “He’s selling three for a fiver” from the visiting enclosure. The reference to selling DVDs is considered to be a racist slur when directed at an Asian person. After Son’s first goal the Tottenham right-back, Kyle Walker, who was an unused substitute, pointed towards the Millwall fans – in an apparent acknowledgment of the chants.

Leicester City had previously complained to the FA about “abuse, provocation and intimidation” of their players, fans and staff in their FA Cup fifth-round defeat by Millwall last month.

The Millwall manager, Neil Harris, said: “I didn’t hear anything [in terms of chants] but, if that’s proven to have happened, we won’t condone that. We want people to be dealt with harshly. We came here in the right spirit to enjoy an FA Cup quarter-final. I’m sure it will be left to the authorities. We just want people to enjoy the game.

“Mauricio Pochettino wants to be talking about his team’s quality and we don’t want anything drawing the focus from what we’ve achieved in this competition. [Incidents like that are] wrong in society, and it’s wrong in football.”

Pochettino, the Tottenham manager, said he had not heard the chants and he added that Son had not mentioned anything in the dressing room afterwards.

The tie had been classified as high-risk and a raft of security measures were put in place. Tottenham closed their club shop; stewards wore hard hats close to the segregation lines on either side of the away end and there were no advertising hoardings inside the enclosure. There were numerous police officers on duty in riot gear while the Met used a helicopter to keep a watch on things.

On the field one of the major incidents was Kane’s injury and the fear is that his season could be as good as over. He left White Hart Lane on crutches with his right foot in a protective boot.

Pochettino said he was worried the damage would prove similar to that which Kane suffered against Sunderland last September. Back then scans revealed a ligament issue and he was out for seven weeks. Kane fell awkwardly after a challenge from the Millwall defender, Jake Cooper, early on and he could not continue after treatment.

“It’s the same ankle as before in the Sunderland game,” Pochettino said. “Now it’s a matter of waiting. We will assess it tomorrow and, after tomorrow, we will see what happens. It’s difficult. It looks a similar situation to Sunderland. It was a similar action. It’s sure it will be difficult for him to play against Southampton on Sunday but we need to wait now and see what happens.

“Harry was in the boot afterwards because in a situation like this, the doctor is cautious. Before a scan, the doctor tries to immobilise the joint, with a boot and crutches – to try to avoid any [further] problems.

“Harry is our main striker, one of the best in England, but we can’t cry about it now. We have enough players to try and replace him. It won’t be an excuse if we don’t win or achieve our aims because Harry is not in the team.”