The solitary blemish comes from a batch of 1,197 tests carried out on players and staff at English top-flight clubs on Monday and Tuesday.
In line with the Premier League's established policy, the club or individual were not initially named, although Spurs swiftly confirmed they were the team in question via a statement.
"We have been informed by the Premier League that we have received one positive test for COVID-19 following the latest round of testing at our training centre," the statement read.
"Due to medical confidentiality, the individual’s name will not be disclosed.
"They are currently asymptomatic and will now self-isolate for seven days, in line with Premier League protocol, before undergoing further testing.
"We shall continue to strictly adhere to the Premier League's return to training protocol, which ensures our training centre remains a safe and virus-free working environment."
The fifth batch of tests represents another encouraging step in the Premier League's preparations to return to action behind closed doors later this month.
There were no positives from 1,130 tests in the fourth round, following four out of 1,008 in round three and two from 996 and six out of 748 in rounds two and one respectively.
The Premier League will restart on June 17 with matches between Manchester City and Arsenal, and Aston Villa and Sheffield United.