In a letter seen by Edinburgh Evening News, headteacher Susan Dunn alerted parents and carers to a positive case at the school over the weekend.
In a second letter sent out on Thursday, 19 November, Ms Dunn has confirmed a second person at the school now has confirmed Covid.
The school will remain open and no other staff or pupils apart from the two who have tested positive have been asked to self-isolate.
Ms Dunn said the school has brought froward its monthly ‘fogging’ process – a system where fine mist containing disinfectant is sprayed into the air to ‘reduce infectious pathogens – to ensure top hygiene measures are in place since the news of the positive tests.
In her letter she explained: “The two cases of Covid we have been dealing with have been contained within one area and this space has been cleaned thoroughly each day by our Facilities Management team.
"The room will remain out of use until the isolation period of those affected has expired."
She went on to urge parents and carers to wear a face mask when entering the school playground after a number have been seen without one on.
"We have sent out several communications regarding this issue and politely request that ALL adults entering our school playground/building wear a face covering,” she added.
"We understand that some people are exempt from this, however anyone without a valid reason for not doing so will be asked to leave the school grounds.
"We must try to ensure the safety of our staff and pupils, wearing a face covering is one way of supporting this.”
During drop off and pick up times Ms Dunn asked parents and carers to also be mindful of social distancing and make every effort to stay two metres apart where possible.
A council spokesman said: “We are working with NHS Lothian’s Health Protection team and parents and the wider school community have been provided with information and reassurance.
"We know that this occurrence may cause concern to some parents and children but we will continue to monitor the situation and follow the advice provided.”