On June 30, 2016, the Marlins traded Paddack to the San Diego Padres for Fernando Rodney.[5] He was then assigned to the Fort Wayne TinCaps. On July 30, 2016, Paddack was diagnosed with a torn UCL. He underwent Tommy John surgery on August 15 and missed the rest of the 2016 season.[6] In nine starts between Greensboro and Fort Wayne, he posted a 2–0 record and 0.85 ERA along with 71 strikeouts.[7] The surgery forced Paddack to also miss all of 2017.
Paddack returned to the mound in 2018 with the High-A Lake Elsinore Storm. With the Storm, he pitched to a 2.24 ERA in 52 innings before being promoted to the AA San Antonio Missions. He was even better for the Missions, pitching to a 1.91 ERA in 38 innings before reaching his innings limit and being shut down for the remainder of the season.[8] The Padres added him to their 40-man roster after the season.[9]
Paddack was invited to spring training by the Padres in 2019 and dominated, pitching to a 3-1 record and a 1.76 ERA in 5 games, earning him a spot on the team's opening day rotation.[10] On March 31, 2019, he made his major league debut with a start versus the San Francisco Giants. He allowed one run over five innings and recorded seven strikeouts. On June 12, 2019, he was optioned to Lake Elsinore as a way to lessen his amount of innings pitched.[11] He was recalled on June 22.[12] During his 2019 season, he earned the nickname "Paddack Attack" for his first-pitch strike-heavy approach and relentless assault on opposing hitters with his fastball and changeup combination.[13][14] Paddack finished with a record of 9-7 and a 3.33 ERA in 26 starts. He struck out 153 in 140+2⁄3 innings. Paddack was named the Opening day starter for the Padres in 2020. He finished 4–5 with a 4.73 ERA. Throughout the season, Paddack struggled with command as he allowed 14 home runs in just 59 innings.
On January 13, 2023, Paddack agreed to a one-year, $2.4 million contract with the Twins, avoiding salary arbitration.[17] Later that day, Paddack agreed to a three-year, $12.5 million contract extension with the Twins that bought out his two remaining arbitration-eligible years and what would have been his first year of free agency.[18] On September 24, Paddack was activated from the injured list to make his return from Tommy John surgery.[19] Paddack began the season in the Twins rotation to begin the 2024 season but suffered through another injury shortened season, appearing in only 17 games before a complete shutdown due to a forearm strain in August. Paddack was 5–3 with a 4.99 ERA and 79 strikeouts over 88+1⁄3 innings pitched.[20]