The Red Devils were set to welcome Preston to Old Trafford on Saturday.
In a statement on their website, United said: "Following routine testing of the first-team training group today (Thursday), we have identified a small number of suspected positive cases.
This has led to those people isolating, pending further tests.
"As a precautionary measure based on COVID protocols, we have taken the difficult decision that we will not now be able to play the friendly match against Preston North End this Saturday (31 July).
"We regret the disruption to Preston North End and disappointment caused to fans.
"Any Manchester United supporters who have purchased tickets for the game will be automatically refunded.
"At this stage, we do not expect further disruption around our forthcoming matches, but we will continue to follow Premier League protocols in this regard."
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