Wimbledon were due to travel to League Two side Barrow on Saturday, but the squad are now self-isolating.
All first-team players and members of the club’s Under-18s squad will now undergo Covid testing.
A statement on the Wimbledon website said: “Saturday’s FA Cup match against Barrow is postponed due to a number of positive results for Covid-19 amongst the first-team group of AFC Wimbledon.
“Testing of all first-team players and staff is now taking place, as well as Under-18 squad members as a precautionary measure.
“The first-team group will now all self-isolate. The match will be rescheduled on a date to be confirmed.”
It is unclear at this stage whether their home match against Wigan next Saturday is under threat.
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