The Los Angeles Dodgers selected Sheehan in the sixth round of the 2021 Major League Baseball draft.[5] After signing with the team he was assigned to the Rookie-levelArizona Complex League Dodgers to start his professional career before being promoted to the Low-ARancho Cucamonga Quakes and then a second time to the High-AGreat Lakes Loons.[6] Sheehan finished the season with a 3–0 record and a 5.17 ERA with 34 strikeouts in 15+2⁄3 innings pitched over seven appearances.[7] He returned to Great Lakes to start the 2022 season.[8] He appeared in 18 games (12 starts) for the Loons and then made two starts after a late season call-up to the Double-A Tulsa Drillers. He had a 7–2 record and 2.91 ERA between the two teams with 106 strikeouts.[6]
Sheehan began 2023 with Tulsa, starting 10 games (12 total) with a 4–1 record and 1.86 ERA. He also struck out 88 batters in 53+1⁄3 innings.[6] He was called up to the majors on June 16 to start against the San Francisco Giants.[9] In his debut, he pitched six scoreless no-hit innings while allowing two walks and striking out three.[10] His first major league strikeout was against Mike Yastrzemski.[11] On June 23, Sheehan picked up his first major league win against the Houston Astros.[12] He started 11 games (and two relief appearances) with a 4–1 record and a 4.92 ERA.[13]
Sheehan was expected to compete for a spot in the Dodgers rotation to start 2024, but was slowed in spring training by shoulder soreness and began the season on the injured list.[14] On May 15, Sheehan underwent Tommy John surgery to repair the ulnar collateral ligament in his elbow, shutting him down for the rest of the season.[15]
