The individuals in question returned positive after a series of routine lateral flow tests on Thursday and are now in isolation awaiting PCR test results.
Ole Gunnar Solskjaer’s side were due to travel to Deepdale on Saturday to face Preston in their fourth preseason friendly, but that trip has now been called off.
A club statement read: “As a precautionary measure based on the Covid protocols, we have made the difficult decision that we will now not be able to play the friendly against Preston North End this Saturday.
“We regret the disruption of Preston North End and the disappointment caused to the fans.
“All Manchester United supporters who have purchased tickets for the match will be automatically reimbursed.
“At this point we don’t expect any further disruption around our next games, but we will continue to follow Premier League protocols in this regard. “
United drew 2-2 with Premier League newcomers Brentford at Old Trafford on Wednesday night, with Anthony Elanga and Andreas Pereira scoring United’s goals.
Solskjaer is currently without several first-team players who have been to major international tournaments this summer, although Harry Maguire, Luke Shaw and Marcus Rashford are due to resume training on Monday.