The University of York said it had been informed by Public Health England (PHE) that one of the two people to test positive for the virus was a student.
The two patients, who are both from China and related, were staying at Staycity apartment-hotel in York before they were rushed to hospital in Newcastle.
The hotel remains open but their apartment will be thoroughly disinfected, the company said.
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Meanwhile, the 83 British people who were evacuated from Wuhan in China have been quarantined Arrowe Park Hospital in Wirral, where they will remain for 14 days.
Coronavirus has caused the deaths of 213 people so far - all in China.
Prof Chris Whitty, chief medical officer for England, said the NHS was "extremely well-prepared for managing infections".