The New York Yankees selected Montgomery in the fourth round, with the 122nd overall selection, of the 2014 Major League Baseball draft. He signed with the Yankees, receiving a $424,000 signing bonus. He pitched for the Gulf Coast Yankees of the Rookie-levelGulf Coast League and the Staten Island Yankees of the Class A-Short SeasonNew York–Penn League, pitching to a 1–1 record with a 3.79 ERA in 19 innings, as the Yankees limited his workload after the college season. In 2015, he began the season with for the Charleston RiverDogs of the Class ASouth Atlantic League. The Yankees promoted him to the Tampa Yankees of the Class A-AdvancedFlorida State League in June. Montgomery began the 2016 season with the Trenton Thunder of the Class AAEastern League and was promoted to the Scranton/Wilkes-Barre RailRiders of the Class AAAInternational League in August. He pitched in the Triple-A National Championship Game, earning the win. Montgomery received a non-roster invitation to spring training in 2017, and competed for a job in their Opening Daystarting rotation. After starting the season at Triple-A for the Scranton/Wilkes-Barre RailRiders, the Yankees promoted Montgomery to the major leagues on April 12, 2017. In his major league debut against the Tampa Bay Rays, Montgomery received a no-decision as he allowed three runs in innings, striking out seven. On April 17, in his second major league start, Montgomery earned his first major league win against the Chicago White Sox. On June 9 against the Baltimore Orioles, Montgomery pitched a career-high seven innings and struck out a career-high eight batters. Montgomery tied those same career highs in a June 26 start against the White Sox. Prior to the All-Star Break, Montgomery pitched to a 3.65 ERA, striking out 87 batters in innings. On July 25, against the Cincinnati Reds, Montgomery took a no-hitter into the sixth inning before Scott Schebler hit a double to break up the bid. On August 6, he was optioned to Triple-A. He was recalled on August 11 after CC Sabathia suffered a knee injury. On August 12, Montgomery was struck in the head by an errant foul ball during batting practice while signing autographs prior to the game; he was not seriously hurt. In 29 starts in 2017, Montgomery finished with a 9–7 record and a 3.88 ERA. On May 1, 2018, Montgomery left a game against the Houston Astros after one inning due to elbow tightness, which sent him to the disabled list the next day with a flexor strain and it was announced he would be out 6–8 weeks. However, on June 5, it was announced that Montgomery tore his ulnar collateral ligament while throwing on flat ground during rehab a few days prior and would undergo Tommy John surgery, ending his season. In six starts in 2018, Montgomery finished with a 2–0 record and a 3.62 ERA. Montgomery started the 2019 season on the 60-day injured list while still recovering from the previous season's surgery. He returned to the Yankees on September 15.
Personal life
Montgomery has two older brothers. He earned the nickname "Gumby" in college after a senior baseball player used the moniker to make fun of his long limbs and lack of coordination.