Alumwell Junior School in Primley Avenue has closed today and will reopen on Monday after staff members reported flu-like symptoms.
The neighbouring infant school and nursery school are open as normal.
In a statement to parents, Executive Headteacher Michelle Sheehy said: "As a precautionary measure, due to the fact that we have several members of staff absent with flu-like symptoms, we have decided to close the school on Wednesday, Thursday and Friday in order to conduct a deep clean of the premises.
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"The school intends to reopen on Monday.
"Please be assured that this is a precautionary measure only and a decision taken by the school following advice from the local authority and health colleagues.
"I’d like to reiterate that good hygiene is the best prevention for the spread of viruses and there are some simple steps you can take to protect you and your family by washing your hands regularly and thoroughly and if you cough or sneeze, cover your mouth and nose with a tissue and bin it. If you or a member of your family have flu-like symptoms please contact NHS 111 and follow advice.
"We will keep you updated by email and on the school website."
So far there have been no confirmed cases of coronavirus in Walsall, although five people have tested positive in Wolverhampton and one person in Dudley.
A woman in her 70s died at New Cross Hospital on Monday and is thought to have contracted the disease in the UK.
Walsall Council is yet to set up a testing facility like the drive-thru one in Wolverhampton but has "advanced" plans ready to introduce one should the virus hit the borough.
A spokesman for Walsall Council said: "Alumwell Junior School is currently closed as they have a number of staff absent with reported flu-like symptoms.
"The school intends to re-open on Monday 16 March after undertaking a deep clean of the premises. This is a normal precautionary measure and a decision taken by the school following advice from Walsall Council."