Premier Mark McGowan said earlier on Monday more than 250 of the 1700-plus passengers had upper respiratory illnesses but the vessel needed to refuel.

Late in the night, the state government said in a statement the ship will refuel in Fremantle on Tuesday morning but no passengers or crew will be allowed to disembark.

WA Police and Border Force will monitor the ship at that time.

Mr McGowan has vowed people on board would not be "walking around the streets".

"I will not allow what happened in Sydney to happen here."

He was referring to 48 cases of coronavirus among Ruby Princess passengers and five from the Ovation of the Seas after docking in Sydney last week.

Magnifica's operator MSC Cruises said the ship, which left Italy in January, planned to make only a "technical call" into Fremantle on its way to Dubai and no one would disembark.

"No passengers or crew onboard suffer from any respiratory diseases or present any flu-like symptoms," the company said.

"There is no evidence to suggest anyone onboard may be infected with COVID-19."

The premier's spokeswoman said his information came from authorities.

In a statement on Monday night, WA said the vessel had given inconsistent reports to both the state and federal governments about the health of its passengers.

Earlier in the day, Health Minister Roger Cook confirmed 20 new cases, including six from the Ruby Princess and one from the Ovation of the Seas, bringing the state's total to 140.

Two are in hospital in a critical condition.

Mr McGowan also announced parents could choose to keep their children home from school but they must not roam shops and beaches.

He said schools would remain open until the end of term one and the state government would provide tools to allow students to continue learning.

Education Minister Sue Ellery said it was "too early to call" any changes to ATAR exams, but processes were in place to ensure year 12 students would not be disadvantaged.

St Andrews Grammar became the first school in WA to temporarily close after a parent of two students tested positive for coronavirus.

The parent is self-isolating with their children, who have not displayed any symptoms.

The Independent Education Union WA branch is backing calls to close all schools immediately, while the State School Teachers' Union of WA wants either pupil free days or holidays brought forward, with both citing factors including insufficient hygiene arrangements.

A University of Western Australia student who tested positive for the virus was self-isolating and had not visited the campus since returning from an overseas exchange, vice-chancellor Jane den Hollander said.

Mr McGowan said too many people were disregarding social distancing directives, urging those doing the right thing to "call them out".

Entry to WA will be restricted on Tuesday but there will be exemptions for workers performing critical duties.

Australian Associated Press