Tight end Tyler Kroft, cornerback Levi Wallace and safety Dean Marlowe were deemed to have been in close contact with Norman and were placed on the reserve/COVID-19 list along with him. None of the four players will travel to Arizona this weekend.
Their absence leaves Buffalo without four players who are either starters or immediate backups at their respective positions.
Norman was set to return to action after missing the past three games with a hamstring injury; it would have been just the second game this season where the Bills had Norman, Wallace and Tre'Davious White active at cornerback.
Kroft has statistically been the team's best tight end this season, with 119 receiving yards and three touchdowns. Without him, the Bills will rely heavily on 2019 third-round pick Dawson Knox.