Victoria has closed its third school in two days after a positive coronavirus test in a student.

Strathmore Primary School, in Melbourne’s north-west, was closed on Tuesday after a year five pupil was confirmed to have COVID-19.

It was one of nine virus cases reported in Victoria on Tuesday, including one more linked to an extended family cluster that has grown to 12.

The family outbreak, which covers five households, also led to the closure of two other Melbourne schools on Monday. Pakenham Springs Primary School, in the city’s south-east, and St Dominic’s in Broadmeadows, in the north, were shut for deep cleaning and contact tracing after pupils fell ill.

Victorian Health Minister Jenny Mikakos said parents at Strathmore were notified late on Monday of the positive test.

“The school is closed today and will be subject to a deep cleaning, and obviously the contact tracing will commence immediately to identify the staff and students who might be impacted by this particular case,” she said.

Despite the rash of school closures, chief health officer Brett Sutton said there was no cause for alarm.

“What’s reassuring for me, and I think for everyone, and it’s been the global picture is that when we look at the classroom contacts of the kids … they don’t pick up illness,” he told Melbourne radio 3AW.

“They’re very unlikely to pick it up from the kids in the classroom.”

Tuesday was the third day of a spike in Victorian infections – with nine cases on Sunday followed by 12 on Monday.

Two of Tuesday’s cases are in an emerging cluster linked to a patient at Monash Health. That outbreak has six confirmed infections.

Also among this week’s new cases are a second Black Lives Matter protester. However, authorities say the woman – who has only mild symptoms and wore protective equipment at the June 6 march – was unlikely to have been infectious at the time.

Elsewhere, NSW reported three new cases on Tuesday morning. All were in people in hotel quarantine.