All pupils in year four at Ocker Hill Academy, in Gospel Oak Road, will now have to stay home for 14 days, starting from September 9.
All staff working regularly in year four will also self-isolate for two weeks.
A letter sent to parents, dated September 9, states: "We have been notified, late this afternoon, that a pupil in Class IW (Year 4) has tested positive for Covid-19. The child in question last attended the academy on Friday, September 4. The child's sibling and parent have tested negative for Covid-19.
"I have spoken to a representative from Public Health England who advised that only children and adults who have had direct contact with the child need to take action.
"While I understand the impact and challenges of the self-isolation period for the year four families, I must stress that these measures have been advised by Public Health England to ensure the safety and wellbeing of everyone at Ocker Hill Academy. We want to put everyone's health first."
The letter adds that siblings and parents of children in year four do not need to self-isolate. And all pupils in years three, five and six also do not need to self-isolate.