On July 10, 2018, Richards left the game early against the Seattle Mariners with "right forearm irritation". The next day, the MRI revealed he had a damaged ulnar collateral ligament in his pitching elbow. He underwent Tommy John surgery, ending his 2018 season and delaying his readiness in the following season. He ended the 2018 season with a record of 5–4 and a 3.66 ERA, while leading the American League with 15 wild pitches.
On December 7, 2018, Richards signed a two-year contract with the San Diego Padres. He appeared in his first game for the Padres on September 16, 2019.
Richards leads with four-seam and two-seam fastballs at mid-90s mph (tops out at 99) with running action. He also has a changeup to lefties, a slider to righties, and a curveball. Joe Girardi, known for serving as manager of the New York Yankees, noted that Richards' fastball is exceptional because "its movement... is not consistent". In 2018, he led the MLB in average spin rate for sliders (2919 rpm) and curveballs (3253 rpm).