According to ESPN's Adam Schefter, Bradford has an active roster bonus of $312,500 per game that he will not collect as the third quarterback.
Rookie Josh Rosen will start Sunday against the Seattle Seahawks after replacing Bradford last week, and veteran Mike Glennon will reportedly serve as the backup.
Schefter noted that if Bradford remains the No. 3 quarterback for the remainder of the season, he will miss out on over $4 million in bonuses, while the Cardinals will save that much against the salary cap.
The 30-year-old Bradford struggled during Arizona's 0-3 start, throwing for 400 yards, two touchdowns and four interceptions.
Following the retirement of Carson Palmer, the Cards signed Bradford to a one-year, $20 million contract during the offseason with a team option for 2019, per Spotrac.
Bradford missed most of last season due to injury, but in 2016 he set an NFL record (since broken by New Orleans Saints quarterback Drew Brees) by completing 71.6 percent of his passes. Bradford also threw for 3,877 yards, 20 touchdowns and just five interceptions for the Minnesota Vikings that season.
He is a ninth-year veteran who was originally selected by the then-St. Louis Rams with the No. 1 overall pick in the 2010 NFL draft.
Despite signing Bradford, Arizona traded up in the first round of the 2018 NFL draft to select Rosen with the No. 10 overall pick.
After replacing Bradford last week, Rosen went 4-of-7 for 36 yards with no touchdowns and one interception.
Rosen will attempt to help the Cardinals avoid their first 0-4 start since 1986.