The man was taken to hospital on Wednesday evening and witnesses saw paramedics wearing quarantine suits treat him at around 8pm.
He was staying at the Staycity aparthotel on Paragon Street, near York Barbican, with two companions when he fell ill.
The man's room has now been cordoned off and the building will undergo a deep clean. It will remain open.
It was earlier reported that the man is a Chinese national but Staycity said they were unable to confirm his citizenship or where he had travelled from.
He has been taken to hospital for further tests.
It is not known whether the man is suspected of being infected with coronavirus, the respiratory condition which originated in the Chinese city of Wuhan. It has now spread across China, with over 7,700 confirmed cases and 170 deaths, and has been reported in 15 other countries.
There have been no confirmed cases in the UK so far but 130 people have been tested for coronavirus, most of them travellers who had recently returned from Wuhan.
York Teaching Hospital NHS Trust would not confirm on whether they were treating the man and Public Health England do not comment on individual cases.
A statement from hotel owners Staycity Group said: "Staycity Group have confirmed that a man staying at the group’s property in York was taken ill yesterday and is understood to be undergoing tests at a local hospital.
"Paramedics accompanied the man, along with his two travelling companions, out of the property at around 7.50pm last night.
"Staycity is unable to confirm which hospital the three people were taken to or what the outcome of the tests are at this point.
"Until more is known the apartment containing the group’s belongings will be cordoned off, along with surrounding rooms, after which the area will undergo a thorough environmental clean and disinfection, as is company policy."