There were six positive Covid-19 tests across three Premier League clubs on Sunday and Monday.
Testing was carried out on just under 750 players and staff ahead of a return to training this week.
The unnamed players or staff who tested positive will now self-isolate for 7 days.
Premier League bosses are hoping to restart the season next month.
Clubs are allowed to resume training this week in small groups, while observing social distancing.
