The remainder of the week would be devoted to transitioning to the new system.
Distance learning would commence Monday and continue until the end of term on April 9.
The school invited families under severe strain to contact them to discuss their situations.
Principal Steven Davies cautioned parents against using older grandpatrents or relatives for childcare during this time.
“As we move into an uncertain time ... we hope that St Mark’s will continue for your family to be a source of stability, strength and learning,” he wrote.
“It is important that we all care for each other and understand that each of us is doing our best in unusual and unprecedented circumstances.”
WAtoday has previously understood from conversations with a senior figure in the independent school sector that schools must wait for a directive, or at least permission, from the state government before they can close despite many having already readied to do so.
St Andrew’s Grammar will be closed for the rest of term after a parent tested positive to COVID-19.
Its principal told Today Perth the school board made the decision for themselves after the Department of Health was "indecisive".