A statement issued by the University on Tuesday claimed reports of racism and abuse had been reported by staff and students after two people were taken ill last week.
No new cases have been confirmed in York.
A joint statement from the University's Vice-Chancellor Prof Charlie Jeffery and presidents of the Students' Union and Graduate Students' Association on Tuesday called for an end to intolerance and ignorance surrounding the disease's outbreak.
The statement wrote: "The University is a global community, with one in every four people on our campus (both staff and students), coming from outside the UK. We value, celebrate and are proud of our inclusive and diverse community.
"Unfortunately, we have had some reports from students and staff of abuse and racism linked to the current coronavirus situation. These instances have occurred both in person and online and we want to condemn these actions in the strongest possible terms.
"Any act of abuse or inflammatory hate speech, whether it occurs on campus, online or elsewhere will not be tolerated.
"We would like to remind all staff and students that the University is a community of respect. All members of our community are expected to act in accordance with our shared values of respect, fairness and compassion, and to ensure that all aspects of our individual and collective behaviour adhere to, and reflect, these principles."
It continued: "We encourage anyone experiencing or witnessing abuse or inappropriate behaviour to report it to the University. If you feel you need support, please contact the Student Hub.
"You can also report incidents to the local police. If you see inappropriate or misleading posts on social media, please report them directly to the service provider (eg Facebook, Twitter, Instagram).
"We must ensure that we continue to be a community where every member accepts their obligations and responsibilities to each other in order to live, learn, work and research in a peaceful and supportive environment. Regulation 7 outlines our expectations and lists disciplinary offences. We will not tolerate behaviour that in any way compromises those expectations."