Gig Mill Primary School closed at the end of today and will now not reopen until Tuesday, November 3.
It comes after the school was made aware of two further members of the school community who have tested positive for Covid-19.
The small number of children and staff who had been in close contact with the positive cases are already self-isolating for 14 days.
A letter sent to parents, seen by the Express and Star, states: "We have been made aware of two further members of our school community who have tested positive for Covid-19.
"We know that you may find this concerning but we are continuing to monitor the situation and are working closely with Public Health England.
"This letter is to inform you of the current situation and provide advice on how to support your child.
"Please be reassured that for most people, coronavirus (Covid-19) will be a mild illness.
"The small number of children who have been in close contact with the individual who has tested positive for coronavirus (Covid-19) have received a letter informing them that their child must stay at home for 14 days.
'Remote learning is available'
"In line with national guidance, and in order to keep all our school community safe, any potential staff contacts will be required to isolate for 14 days.
"Therefore the local authority have agreed and support the closure of Gig Mill Primary School from the end of the school day today [Wednesday].
"School will reopen on Tuesday, November 3.
"Over this period please continue to advise school via the email@example.com if anyone in your household develops symptoms as outlined below.
"Remote learning is available on our school website."