At the 2019 NFL Combine, Montez set a combine record for a defensive lineman running the 40 yard dash at 4.41 seconds.[7] At the same time, Sweat was diagnosed with hypertrophic cardiomyopathy at his combine health physical.[8] However, it was soon discovered to have been a misdiagnosis due to an improper measuring of his heart.[9] Sweat was eventually selected by the Washington Redskins in the first round, 26th overall, of the 2019 NFL draft.[10] The team traded back up into the first round to select him after using their original pick on Dwayne Haskins.[9] He signed his four-year rookie contract on May 29, 2019,[11] worth $11.6 million, including a $6.4 million signing bonus.[12] In Week 3 against the Chicago Bears on Monday Night Football, Sweat recorded his first career sack in a 31–15 loss.[13] In Week 17 against the Dallas Cowboys, Sweat sacked Dak Prescott twice, one of which was a forced fumble that was recovered, during a 47–16 loss.[14]
In a game against the Dallas Cowboys on Thanksgiving in 2020, Sweat intercepted a pass thrown by Dalton late in the fourth quarter and returned it 15 yards for a touchdown that led to a 41–16 Washington victory.[15][16] The following week against the Pittsburgh Steelers, Sweat tipped a pass late in the fourth quarter that led to an interception by Jon Bostic to help secure a 23–17 win over the then-undefeated Steelers.[17] In Week 15 Sweat batted a pass by Seattle Seahawks quarterback Russell Wilson which was then intercepted by Daron Payne.[18]
Sweat suffered a jaw fracture during a Week 8 game against the Denver Broncos in 2021 and was placed on injured reserve.[19][20] After testing positive, he was placed on the COVID-19 reserve list on December 8, 2021.[21] On December 18, he was taken off the COVID-19 list and placed back on the active roster two days later.[22][23] In the Week 15 against the Philadelphia Eagles, Sweat recorded a sack and forced a fumble, which was recovered by Landon Collins, on quarterback Jalen Hurts.[24]
On April 27, 2022, the Commanders exercised the fifth-year option in Sweat's contract.[25] In Week 5, Sweat accounted for two of the five sacks the Commanders' had against the Tennessee Titans.[26] He contributed another two sack performance against the Houston Texans in Week 11.[27]
Chicago Bears
On October 31, 2023, Sweat was traded to the Chicago Bears for a second-round pick in the 2024 NFL draft.[28][29] Four days later, he signed a four-year contract extension worth $98 million, including $72 million guaranteed.[30][31] He recorded his first sack as a Bear in Week 11 against the Detroit Lions in their 31–26 loss. On January 3, 2024, Sweat was named a Pro Bowler for the first time.[32] He finished the season a career-high 12.5 sacks across two teams in 2023, collecting 6.5 while with the Commanders before adding another 6 with the Bears.[33] He became the first player in NFL history to lead two teams in sacks during a single season.[33]Matt Eberflus, the Bears head coach, referred to Sweat's impact as the "'Tez effect", which allowed the other players around him to generate more sacks, quarterback pressures, and turnovers.[33][34]
Sweat was raised by his grandparents as a child.[35] Both his mother and older brother died in 2021, the latter being killed at the age of 27 in a shooting in Henrico County, Virginia.[36] As a rookie, Sweat was featured in Old Spice television commercials.[37]
In June 2021, Sweat expressed his disinterest in getting vaccinations against the COVID-19 virus and that he would forgo getting a COVID-19 vaccine.[38]