Despite the decision, Cavani was initially selected for Oscar Tabarez's squad for its three FIFA World Cup qualifiers against Peru, Bolivia and Ecuador.
Both Uruguay and Peru are on the United Kingdom's red list, meaning the 34-year-old would have had to quarantine for 10 days in a hotel upon his return from South America.
Tabarez has opted to cancel the call-up due to the fact the United forward would subsequently miss at least two top-flight games against Newcastle United and West Ham and the Champions League match with Young Boys.
The announcement comes after Aston Villa and Tottenham confirmed they would let their Argentinian contingent travel, while Liverpool remained firm in not letting their Brazil trio leave nor Egypt forward Mohamed Salah.
Indeed, United manager Ole Gunnar Solskjaer urged Cavani to stay loyal to the club last weekend, warning his striker that he risked making himself unavailable should he travel.
Meanwhile, United prospect Amad Diallo will also be staying in Manchester after his proposed loan move to Feyenoord was cancelled due to a thigh injury sustained in training. The 19-year-old is set to be out for up to six weeks and will undergo rehabilitation in England.
Speaking to Dutch outlet AD, Feyenoord's technical director Frank Arnesen confirmed: "He got injured, it [the loan] is cancelled.
"Too bad, everything was done. I've talked a lot with the people at Manchester United, but it's more sensible to let him recover at that club. It may be a while before he is back."