Bradford is wearing red and white for the AFC Championship game against the New England Patriots.
The Patriots were forced to replace defensive tackle Vince Wilfork with Ryan Wendell on Tuesday after the injury.
Wilfork, a seventh-round pick of the New York Jets in 2015, tore his ACL in a loss to the Cincinnati Bengals.
The team did not say how many days Wilfork will miss.
Wilkinson, a four-time Pro Bowler, has started two games for the Patriots this season.
Brady, who was a part of the Super Bowl XLVI team that defeated the Miami Dolphins, will take his first start of the season on Sunday against the Denver Broncos.
The Patriots are coming off a win over the Chicago Bears on Sunday.
Brady and the Patriots will play their first game of the 2017 season at the New Jersey Memorial Coliseum.