An Asian doctor at Melbourne's Royal Children's Hospital was told by family to stay away from a child she was treating amid fear of the coronavirus outbreak.

A doctor of Asian appearance at a Victorian hospital was told by parents to stay away from a child amid fears of the coronavirus, while other staff and patients have reported discrimination.

Royal Children's Hospital director of emergency, Stuart Lewena, said a doctor was told by parents of a child she was treating they were not comfortable with her.

"It was clear that message was sent on the basis of her race. We intervened to highlight to that family that wasn't acceptable and we've been supporting that staff member," Dr Lewena said on Thursday.

The doctor continued to treat the patient but the situation required the intervention of a senior staff member, Dr Lewena said.

"The message was given that we have complete confidence in that staff member and she should remain as one of the treating clinicians for that child."

The doctor took a brief period of time off but is now back at work, Dr Lewena confirmed.

After the incident had been flagged to all staff, Dr Lewena said three more staff members came forward to say they had had similar experiences.

"We want to use this as an opportunity to say that's not acceptable in health care and it's certainly not acceptable in our society," Dr Lewena said.

"Paranoia around coronavirus is acceptable, but we need to be sensible and respectful in terms of how we go about dealing with it."

Victorian Premier Daniel Andrews described the racism as "shameful".

"There is no place for that in Victoria, there is no place at all," he said on Thursday.

The government says the outbreak in mainland China is of concern but the risk of exposure to coronavirus in Victoria remains very low, and certainly has nothing to do with a nurse, doctor or patient's ethnicity.

"We are aware of at least one other hospital where patients presenting have refused to sit near other patients that they have seen of Asian appearance," Victorian Health Minister Jenny Mikakos told reporters.

"That is very concerning. There is no place for this behaviour in our public hospitals, there is no place for this in our broader community."

Victorian Chief Health Officer Dr Brett Sutton said coronavirus preparations are ongoing.

"We're going to work extremely hard on our planning. We are continually adapting to new information and circumstances as they arise," he said.

There are seven confirmed coronavirus cases in Victoria, three of whom are currently in isolation after being evacuated from the Diamond Princess cruise ship and four who have recovered.