"The Premier League can today confirm that between Monday 21 September and Sunday 27 September, 1,595 players and Club staff were tested for COVID-19. Of these, there were 10 new positive tests," the league said in a statement on Monday.
"Players or Club staff who have tested positive will self-isolate for a period of 10 days."
West Ham were hit with three positive tests for manager David Moyes and players Issa Diop and Josh Cullen ahead of their League Cup game against Hull last midweek.
Manchester City also announced last week that German midfielder Ilkay Gundogan had contracted the virus.
Until now the highest number of positive cases recorded in a week by the Premier League was six, when clubs returned to training in May.
A rise in infections across the United Kingdom has seen the reintroduction of stringent measures to curb the spread of Covid-19, including the delay of a return for fans to watch sports events live in stadiums.