Swiss Xhaka, 24, is believed to have been with a friend who had visited him in London and was returning home.
The man is understood to have arrived late for his flight back to Germany and was not allowed to board.
It is at this point that the racial abuse is alleged to have occurred.
Arsenal have declined to comment other than to say it is a private matter that is now in the hands of the police.
A spokesman for the Metropolitan Police told the BBC: "Police were called at 19:29 GMT on Monday, 23 January following an allegation that a member of staff had been racially abused at Heathrow Airport, Terminal Five.
"The allegation was made by a third party. Officers attended and spoke with a man in his 20s. He was not arrested. He voluntarily attended a west London police station where he was interviewed under caution. Enquires continue."
The incident occurred just over 24 hours after Xhaka was sent off during his team's 2-1 victory over Burnley in the Premier League.
Arsenal midfielder Granit Xhaka has been interviewed under caution by police following an allegation he racially abused an airline staff member at Heathrow on Monday night.