Jacksonville Jaguars
The Jacksonville Jaguars selected Minshew in the sixth round, 178th overall, of the 2019 NFL draft. After being drafted, Minshew spent the Jaguars' training camp in competition with Tanner Lee and Alex McGough for a chance to back up starting quarterback Nick Foles. After both Lee and McGough were cut in August, Gardner won the job despite an unimpressive preseason, with the understanding that Foles would receive the majority of starts.
In Week 1 against the Kansas City Chiefs, Minshew made his NFL debut when Foles fractured his left clavicle in the first quarter of game. He completed 22 of 25 passes for 275 yards, two touchdowns, and one interception in the 40–26 loss. His 13 consecutive completed passes were the most of any debuting quarterback since at least 1979, and Minshew's 88 percent pass completion was the highest of any NFL player with at least 15 pass attempts in his debut. With no timetable for Foles' return and no third quarterback, Minshew became Jacksonville's starter. After narrowly losing to the Houston Texans in Week 2, Minshew picked up his first NFL win in Week 3, completing 20 of 30 passes for 204 yards in the 20–7 victory over the Tennessee Titans. Through his first three games, Minshew's 73.8 completion percentage and 110.6 passer rating were the highest of any NFL quarterback in that same time frame. Minshew had a 4–4 record, 2,285 yards, 13 touchdown passes, four interceptions, and a 92.8 passer rating by the time that Foles was activated from the injured reserve on November 5 to take back the starting quarterback role.
Foles struggled in his return, with only two touchdown drives in three games. While facing the Tampa Bay Buccaneers on December 1, he was benched at halftime in favor of Minshew. Although the Jaguars lost 28–11, unable to recoup their first-half deficit, Minshew completed 16 of 27 passes for 141 yards and successfully led the team to two scoring drives. The next day, Jaguars' coach Doug Marrone announced that Minshew would start the Week 14 game against the Los Angeles Chargers. Despite losing to the Chargers 45–10, Minshew was 24 for 37 with 162 yards and one touchdown; his one touchdown, the 15th of the year, set a Jacksonville franchise record for most passing touchdowns by a rookie quarterback. In his next game, Minshew was 17 of 29 with 201 yards and two touchdowns in a 20–16 comeback victory over the Oakland Raiders, the last game to be played in the Oakland Coliseum; he described seeing "more middle fingers today than I have in my whole life" after steering Jacksonville towards victory. Minshew and the Jaguars closed out the season with a 38–20 win over the Indianapolis Colts, during which Minshew threw for 295 yards and three touchdowns. Appearing in 14 games for Jacksonville as a rookie, Minshew had a 6–8 record for the year, with 285 completions in 470 attempts (60.6 completion percentage), 3,271 passing yards, 21 touchdowns, six interceptions, and a 91.2 passer rating. He also had 344 rushing yards in 67 carries.
Foles was traded to the Chicago Bears in March 2020 in exchange for a fourth-round selection in the 2020 NFL draft, paving the way for Minshew to take over as the Jaguars' starting quarterback in the 2020 season. Joshua Dobbs, meanwhile, was acquired from the Pittsburgh Steelers as Minshew's new backup. While defeating the Colts 27–20 in the first game of the season, Minshew completed 19 of 20 pass attempts for 173 yards and three touchdowns, becoming the first NFL quarterback to throw for three or more touchdowns with a pass completion rate of 95 percent or higher. Although he threw for 339 yards and three touchdowns in Week 2 against the Titans, Minshew was also sacked twice, and the game-winning play of the 33–30 loss came on an interception by Harold Landry. His poor Week 3 performance against the Miami Dolphins, throwing 30 of 42 for 275 yards with a fumble and an interception in the 31–13 loss, led to accusations that the Jaguars were tanking their season.
During an October 11 loss to the Texans in which he threw for 301 yards and two touchdowns, Minshew suffered multiple fractures and a strained ligament in his right thumb, a series of injuries through which he continued playing until Jacksonville's 39–29 loss to the Chargers on October 25. X-ray exams after that game revealed the extent of Minshew's injuries, which helped to explain his uncharacteristically poor performance through the first half of the season. At the time, he had a 65.9 percent pass completion rate, five interceptions, and three lost fumbles. In Minshew's absence, Mike Glennon took over as Jacksonville's starting quarterback, a role that he maintained even after Minshew was activated from the injured reserve. Glennon struggled in his Week 13 start, however, and he was pulled halfway through the third quarter of the Jaguars' Week 14 game in favor of Minshew. At that point, the Jaguars were trailing the Titans 31–3 and Minshew led the only Jacksonville touchdown drive in the game. Minshew started in Week 15 against the Baltimore Ravens, throwing for 226 yards and two touchdowns in a 40–14 loss, extending Jacksonville's losing streak to 13 games. Glennon was chosen to close out the season, starting the last two games against the Chicago Bears and Indianapolis Colts, respectively. Overall, Minshew appeared in nine games for the Jaguars during the 2020 season, recording 2,259 passing yards, 16 passing touchdowns, and five interceptions, as well as 153 rushing yards in 29 carries.