Minshew used his final year of eligibility with the Washington State Cougars, setting the Pac-12 Conference season records for passing yards and completions and winning the Johnny Unitas Golden Arm Award.

Minshew was selected in the sixth round of the 2019 NFL draft by the Jacksonville Jaguars, where he played his first two seasons and set the franchise record for rookie passing touchdowns.

Following two seasons as a backup with the Philadelphia Eagles, he became the starter for the Indianapolis Colts in 2023 and earned Pro Bowl honors after setting several career highs.

[2] The next year, Minshew helped take the Brandon Bulldogs to the Mississippi High School Activities Association (MHSAA) 6A championship game, where they lost 31–23 to South Panola.

[12] In addition to describing the university as a poor fit,[13] Minshew found it unlikely that he would unseat starting Trojans quarterback Brandon Silvers, and he began to look for other opportunities.

[14] He completed 21 of 31 passes for 332 yards, including a 61-yard touchdown, in his NJCAA debut and was named the Mississippi Association of Community & Junior Colleges (MACJC) Offensive Player of the Week.

[23] On May 3, 2016, Minshew signed a grant-in-aid with East Carolina University, which enabled him to continue his football career with the Pirates at the NCAA Division I level.

[24] He made his East Carolina debut in Week 1, relieving Nelson midway through the third quarter of a 47–29 loss to Central Florida after the other quarterback suffered an injury.

[32] With Nelson still injured the next week, Minshew started in his first game for East Carolina on November 19, completing 16 of 25 for 238 yards and three touchdowns in the 66–31 loss to the Navy Midshipmen.

[38] Minshew played his first full game of the season on September 16, completing 11 of 30 for 241 yards, two touchdowns, and one interception, including another 76-yard pass to Brown, in the 64–17 loss to Virginia Tech.

[49] Minshew had reportedly not expected to play for Alabama, but used the announcement to draw interest from other schools,[50] at which point Washington State head coach Mike Leach called him and asked, "You want to come lead the nation in passing?

"[51] Tyler Hilinski's January suicide had left the Cougars without a starting quarterback for the 2018 season, and Minshew was placed into competition with rising juniors Trey Tinsley and Anthony Gordon for the role.

[68] As a quarterback whose style of offense prioritizes passing over rushing, his 40-yard dash speed at the combine did not stand out; coaches from various National Football League (NFL) teams also inquired as to why Minshew had attended four different colleges in as many years.

[71] He was also confident that the popularity of other passing-heavy quarterbacks like Patrick Mahomes, Jared Goff, and Baker Mayfield in the NFL would help his stock in the upcoming draft.

[62] 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.

[77] After both Lee and McGough were cut in August,[78][79] Gardner won the job despite an unimpressive preseason, with the understanding that Foles would receive the majority of starts.

[80] 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.

[86] 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.

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.

[94] 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.

[97] 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.

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.

[111] Minshew was asked to start again in the Eagles' regular-season finale against division rival Dallas Cowboys, giving Hurts an opportunity to rest before the 2021–22 NFL playoffs began the following week.

[112] Passing primarily to other reserve players on a roster that had been diminished by COVID-19 protocols, Minshew threw 19 of 33 for 186 yards, with two touchdowns and an interception, while the Eagles lost 51–26 to the Cowboys.

[125][126][127] Minshew was named the starting quarterback for the Colts after Richardson suffered an AC joint sprain in Week 5 against the Tennessee Titans; the latter was placed on injured reserve for the remainder of the season.

[132] In Week 2, Minshew rallied the Raiders to an upset road victory over the Ravens, orchestrating three scoring drives in the fourth quarter to overcome a 10-point deficit.

[134] In Week 7 against the Los Angeles Rams, Minshew replaced an injured O'Connell during the first half and committed four turnovers in relief as the Raiders lost 20–15.

My motto these days is ‘too blessed to be stressed’ and I'm just enjoying every step of this journey.”[141] Outside of football, Minshew is known for his distinctive physical appearance and exercise habits, which have generated several nicknames.

[146][147] His decision to wear aviator sunglasses and a flight jacket before his first game at Lincoln Financial Field also drew comparisons to the film Top Gun.

[148][149] Minshew was also given the nickname "Jock Strap King" by former-Jacksonville running back Leonard Fournette, after the quarterback's propensity for exercising in nothing but the eponymous underwear.