Years One, Six and Reception classes returned to the classroom on Monday 1 June.
Since then two school staff have been confirmed positive, while two results have come back negative and eight are still waiting, according to Lincolnshire County Council.
The affected schools are in Lincoln, Boston, Gainsborough and Grantham.
Two Lincoln schools have already confirmed cases, with one closing completely and the other sending a "bubble" of classmates and teachers home.
On Friday, Bishop King Church of England primary school closed after a member of staff tested positive for coronavirus.