The League One club were also due to face Crewe Alexandra but that game has been suspended.
A club statement read: “Given a number of positive COVID tests on Thursday morning amongst staff members, the Chairman decided that, in the interests of safety of all personnel, the stadium should be closed immediately and staff asked to return to their homes.
“Saturday's home game against Crewe has been postponed due to players testing positive for COVID-19.”
Burnley eyeing Dan Neil deal
Burnley are said to be interested in signing Dan Neil from Sunderland during the January transfer window.
The interest comes after the Clarets watched the England youth international in action against Arsenal in the Carabao Cup.
The Sun state that the Premier League club are ready to bid £3 million for the Sunderland midfielder.
Burnley are reportedly open to signing the 20-year-old during the winter window and then letting him stay on loan at the Stadium of Light for the rest of the campaign.
Sunderland announced last October that Neil had signed a new four-year deal on Wearside.
At the time, Neil said: “Everyone knows that I love this football club and I love playing for it.
"It’s a dream come true to be playing in the first team and I’m loving every minute of it, but I want more and I want to be playing in the higher divisions for Sunderland.
"I want to be part of getting this club back to where it belongs and there’s nowhere I would rather be, so I’m delighted to have extended my contract.”