Benfield Primary School, in Old Shoreham Road, emailed parents today (October 21) to advise the school would be closed from the end of today until Tuesday, November 3.
The email said those who had been in close contact with the staff member had been informed and asked to self-isolate for 14 days.
Due to the number of staff impacted, the email said, the school cannot be opened safely.
Children will not have to self-isolate, the school said, as there was no evidence they had been in close contact on Monday (October 19), when the staff member may have been contagious.
"The two cases do not seem to be related," said the email.
"We know that you may find this concerning, but we are continuing to monitor the situation and are working closely with Public Health England.
We do understand that this is a worrying time, please be assured that we have followed all guidelines and that the school is now being deep cleaned in preparation for reopening on November 3."
Learning would still be provided online, the email added.
If children develop symptoms of Covid-19, NHS advice is to stay at home for at least 10 days from the date symptoms first appeared.