The pupil is self-isolating and there are no known links to the case.
All parents and staff of the school have been notified and the school plans to open as normal today (Tuesday, August 25).
However, as a precautionary measure, NHS Lanarkshire said all pupils and staff in Stepps Primary School Primary 1B have been categorised as contacts of a case and therefore are being asked to self-isolate for 14 days.
Other household members, including siblings at school, are not being asked to self-isolate unless they are showing symptoms of Covid-19.
The health board said there is currently no evidence to suggest that there is transmission in the school and the risk to the wider school community has currently been assessed as low.
They added this is backed up further by the fact that the recent community-wide investigation into the Covid-19 cases at St Ambrose, St Andrews and Caldervale high schools has now been stood down as there have been no new cases over the last week.
Dr Josephine Pravinkumar, NHS Lanarkshire consultant in public health medicine, said: “NHS Lanarkshire’s Test and Protect service is working closely with North and South Lanarkshire Councils and the schools to identify all close contacts of the cases who are being given public health advice and being told to self-isolate.
“There is evidence that mixing socially in the community, particularly around social gatherings in houses, without maintaining physical distancing measures can transmit the virus. It is therefore important that people remain vigilant and follow physical distancing guidance.
“We are aware that there will be concern among both children and their parents at this time. We would like to reassure the local community that appropriate measures are being implemented.
“Individuals should stay off school or work and get tested if they or their close contacts experience any Covid-19 symptoms, such as a cough, fever or loss of taste or smell, even if they are mild.”
Information on how to access testing is available from NHS Inform.
The Incident Management Team continues to meet daily. The health board said respect and maintain patient confidentiality, no further details will be released at this time.