The unnamed student has not been on campus since being infected and was not there in the period beforehand either, a spokesman for the University of York confirmed on Saturday evening.
He stressed the risk to staff and students is therefore low.
The pair - who are related - remain the only two confirmed cases in Britain of coronavirus, which has killed more than 250 people in China.
University of York's Vice-Chancellor, Professor Charlie Jeffery, called for people to respect the privacy of the pair, who are now under the care of the NHS.
A statement posted on the university's website added: "We are continuing to monitor the situation closely and we will continue to provide as much advice, care and support as we can to anyone affected by this situation, and as directed by Public Health England.
Shortly after confirming a student is one of the two confirmed UK cases, the vice-chancellor acknowledged the "concern and anxiety" among students and staff.
But he said: "I want to reassure our students, staff and the wider community that we are working closely with the lead agency, Public Health England, and other agencies to manage this situation."
Public Health England (PHE) is continuing to try and trace people who had close contact - defined as being within two metres for 15 minutes - with the pair, who had checked in to the Staycity apartment-hotel in York and are now being treated at a specialist unit in Newcastle.
A total of 201 tests for coronavirus in the UK have been confirmed negative, the Department of Health said in the latest figures released on Saturday afternoon.