The pair - two members of the same family - are being treated at a specialist unit in Newcastle.
They had checked in to the Staycity apartment-hotel in York on Wednesday and were taken to hospital that evening.
In a statement on Saturday a spokesman for the university said the risk of the infection being passed on to other people on campus is low.
He said: "We understand this development will cause concern and anxiety among our students, staff, and the wider community.
"PHE (Public Health England) has advised us that the risk of infection being passed to others on campus is low.
"Current information from PHE suggests that the student did not come into contact with anybody on campus whilst they had symptoms, but investigations are ongoing to fully establish this.
"Our immediate concerns are for the affected student and family, along with the health and continued wellbeing of our staff, students and visitors."
The hotel firm has said the apartment involved has been thoroughly disinfected and PHE has been providing support.
The two patients are being treated by Newcastle upon Tyne Hospitals NHS Foundation Trust in its specialist Airborne High Consequences Infectious Disease Centre (HCID).
Professor Sharon Peacock said PHE is contacting people who had close contact - defined as being within two metres of the infected person for 15 minutes - with the pair.