The unnamed players or staff who have tested positive from the 748 total tests conducted will now self-isolate for seven days.
Squads are starting non-contact training from Tuesday.
The Premier League has been suspended since 13 March because of the Covid-19 pandemic, with 92 fixtures remaining.
The league had previously identified 12 June for matches to possibly start again, but there is now an expectation this will need to be pushed back.
"The Premier League is providing this aggregated information for the purposes of competition integrity and transparency," it said in a statement.
"No specific details as to clubs or individuals will be provided by the league and results will be made public in this way after each round of testing."
At Monday's "Project Restart" meeting, English top-flight clubs agreed to stage one of the return-to-training protocols.
As well as training in small groups of no more than five, sessions must last no longer than 75 minutes for each player. Social distancing must be adhered to.