Long Meadow School, in Shenley Brook End, has alerted parents in two separate letters that its Year 2 teaching staff tested positive for the virus.
The school said one member of staff initially tested positive over the weekend (September 5-6) and was instructed to self isolate by the school and Public Health England.
Then, on Wednesday (September 9), another member of the Year 2 teaching staff tested positive, but, the school said, they were already self-isolating after the first teacher contracted the virus.
The classroom was deep-cleaned over the weekend and re-opened to students on Monday (September 7) after PHE deemed it safe for the children to return - with the school saying 'there is no greater risk to the children than before'.
As children only returned to school on Monday from their summer holiday, and the first case was confirmed before then, the year group staff were all self-isolating and did not come into contact with their students.
Headteacher Philip Gray said in a letter to parents: "By acting early, we were able to ensure this second staff member was not in school at any point with the children whilst they were infectious.
"All of our Year 2 team are now isolating. All of our staff have been socially distancing within their consistent groups, so it is only this year group’s staff that needed to isolate.
"However, as two members of the school community have now been affected this will now be formally classified as a school outbreak, despite the school not being open to pupils when
Year 2's classes are now being taken by Mrs Browne and Mr Roe, who were in a different year group bubble but have now joined Year 2's 'consistent group'.
Mr Gray said: "We have been working with PHE and Milton Keynes Council to continue to ensure that we have the appropriate systems and measures in place to keep all of school community as safe as possible.
"Based on the advice, risk to pupils remains low and has not changed since my previous letter. There is no greater risk to children than before."