Carey Baptist Grammar School will become the first Victorian school to shut its doors because of the widening coronavirus crisis.

An email from principal Jonathan Walter sent to parents about 7.30 on Monday night said the entire school would be closed to staff and students on Tuesday after an adult member of its community developed symptoms consistent with COVID-19.

The email said the person with symptoms, who is now being tested, had recently been in direct contact with someone confirmed as having the coronavirus.

The school leadership made the decision on Monday to close Carey Grammar, one of Melbourne's most exclusive private schools, while it assessed the situation, the letter said.