Telford & Wrekin Council has confirmed that two classes and four staff at Old Park Primary, in Brunel Road, Malinslee, were at home as a result.
The letter stated that the affected adult was based in the site's Haughton Hub and that the youngsters who were believed to be in year three must stay away until October 14.
"Unless the children in that class have symptoms, then their brothers and sisters can come into school as usual," the school stated.
Parents were informed of the situation in a letter on October 4.
Meanwhile a pupil at Newport's Burton Borough School, is believed to be self-isolating after a positive test.
In a letter the Audley Avenue school stated on Friday that the pupil had not attended for a week and it was believed that they contracted the virus from a family member.
The school added that following advice from the borough's health protection hub no class bubbles were due to be closed as a result.