The sixth-round pick could go to a fifth-rounder if Minshew plays in 50 percent of the plays in three games this season, per sources.
The move comes after Jaguars coach Urban Meyer announced Wednesday that top overall pick Trevor Lawrence had won the starting job and will be under center for the Sept. 12 season opener in Houston against the Texans.
Minshew, who had been alternating practice days with the first-team offense with Lawrence throughout training camp, completed 17 of 29 passes for 196 yards with two interceptions (one in the end zone) in two preseason games.
C.J. Beathard is now in the top backup spot behind Lawrence. Beathard has completed 22 of 30 passes for 223 yards and three touchdowns in the two games.
Minshew replaced an injured Nick Foles as a rookie in 2019 and was brought back as the starter later that season after Foles struggled. That earned him the starting job in 2020 and he started the first seven games of the season before a thumb injury, which he at first hid from the coaching staff, put him on the bench.
Minshew got back on the field for two games in December but finished the season on the bench. After a 1-15 record, the Jaguars hired Urban Meyer and drafted Lawrence, the fan-anointed savior of the franchise.
For his career, Minshew has completed 501-of-797 passes for 5,530 yards with 37 TDs and 11 interceptions.