As a result of the diagnosis of the Strood Academy employee, three other members of staff have been advised to self isolate.
Richard Taylor from the Leigh Academy Trust, which runs the school, said: "We can confirm that a member of support staff at the Academy has tested positive for Covid-19 today and as a result we have been liaising with Public Health England to ensure that all necessary steps are taken to prevent any further transmission across the academy.
"As a result of contact tracing we have advised that three other members of staff should self isolate as a precaution for the next 14 days.
"Public Health England have confirmed that there are no further measures we need to take at this stage and the academy can remain open operating under the Covid secure procedures already in place.
"Staff and parents have been informed as a precaution although the member of staff has not been in close contact with anyone else in the academy. "
With 1,403 on its roll, it is one of Medway's largest secondary schools.
The school opened in 2009, following the closure of Chapter Girls' School and Temple Boys' School, both in Strood.
In 2012, the academy moved into new purpose-built premises in Carnation Road.
Other schools in the Leigh Academy Trust are Hundred of Hoo, Stoke Primary Academy, High Halstow Primary Academy, Allhallows Primary Academy and the Math School, Rochester.