The fixture was scheduled to take place at Chesterfield’s Technique Stadium on Wednesday evening but will now not go ahead following the test results.
“The decision was made as a precautionary measure following a small number of positive COVID-19 test results within City’s first team group,” a Norwich statement read.
“The club’s players and staff will continue to follow Premier League protocols and government guidelines, operating and training in their respective first team bubble at the Lotus Training Centre.”
The Canaries – who are preparing for their return to the Premier League having won the Sky Bet Championship last season – have already played King’s Lynn Town, Lincoln and Huddersfield in pre-season.
Daniel Farke’s side will now face United on Saturday before playing Gillingham and Newcastle ahead of their season opener.