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.

About seven miles (11km) of shoreline, including beaches at Great Yarmouth, Gorleston and from Scratby to North Denes, were affected by the flooding.
On Scratby beach alone, it is believed there are about 6,000 sq metres (65,000 sq ft) of waste, 3ft deep (1 metre).
The operation is expected to take several weeks.
Before Christmas, staff from Great Yarmouth Borough Council took away any potentially hazardous material, including gas bottles, fridges and freezers.
Now workers are left with glass, wire and wood to dispose of.
George Jarvis, from Great Yarmouth Borough Services, said a lot of manpower was being used to sift through the debris.
"We did consider burning on the beach, but looking at the weather forecast we're due to have quite a lot of wet weather this week," he said.
"Also the prevailing winds coming in from the sea would have blown quite a lot of thick, black smoke into public areas."
There is no estimate for the total cost of the clear-up, as it is not yet known how long it will take.
The council hopes to recoup the money spent through the government's Bellwin Scheme.
The Bellwin Scheme was introduced in the 1980s to provide some government support for flood-hit areas, but only provides funds for temporary flood measures and the work must be undertaken within two months of the flood.

Robert Boyd-Stevenson, 38, of Headford Road, Bristol, had admitted a charge of making a bomb hoax by communicating false information last year.
He texted security threats to a phone linked to the airport on 29 August.
The airport remained open but raised its security threat level and police officers were called to the scene.
Days earlier, Bristol Airport had been evacuated in a separate, unconnected bomb scare.
CCTV footage showed Boyd-Stevenson topping up the phone in Knowle West at 05:39 that morning and in the airport itself at about 06:00 BST.
He was sentenced at Bristol Crown Court on Thursday.
PC Simon Broad said the "strength of evidence against him" had meant Boyd-Stevenson admitted his guilt early on.
"Robert Boyd-Stevenson intended to cause disruption to staff and passengers at Bristol Airport, as well as the emergency services, through his reckless actions," the officer said.
A spokesman for the airport said the sentence would send "a strong message" about making bomb threats.
He added: "Only the prompt and professional action of Bristol Airport staff and Avon and Somerset Police on the day prevented significant disruption to the travel plans of thousands of passengers."
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.
[NEXT_CONCEPT]
Work has begun to clear up hundreds of tonnes of waste washed up on Norfolk beaches during last month's North Sea tidal surge.
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A man who made bomb threats to Bristol Airport in a series of text messages has been jailed for two-and-a-half years.