The Blades will now seek alternative opposition for their final game before they start their Championship campaign at home to Birmingham City in the late August 7 kick-off.
Norwich had been due at Bramall Lane on Saturday for new manager Slavisa Jokanovic's first home match in charge. He has overseen friendly wins against Europa Point and Doncaster Rovers.
But Norwich cancelled Wednesday's scheduled friendly at Chesterfield due to "a small number of positive Covid-19 test results within the Norwich City first-team group", and Saturday's game has now fallen victim too.
The Blades' pre-season preparations were disrupted when two of their players tested positive for Covid-19 on the tour of Spain. They had to stay behind whilst their team-mates isolated for 10 days.
Meanwhile, the Blades have confirmed the departure of Alan Knill.
Knill and Chris Wilder reversed the roles they had at Bury when he became Wilder's assistant at Northampton Town then, in 2016, Sheffield United.
Knill declined an off-the-field role when Wilder was sacked in March, and will now leave the club with immediate effect.
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