Murphy began baseball-related activities at the age of four, when his father Mike signed him up for a class offered by the Riverside Recreation Department.[1] Mike Murphy became his son's coach in Little League and travel league baseball when Owen was seven.[1] When he was 13, Murphy began the Rake City baseball training program.[1] Murphy attended Riverside Brookfield High School. He played high school baseball as a pitcher and shortstop,[2] and was also a quarterback and wide receiver for the football team.[1][3] During his junior season in 2021, he pitched to a 6–1 record and a 0.33 ERA alongside hitting nine home runs.[4] As a senior in 2022, he went 9–0 with a 0.12 ERA, surrendering ten hits while striking out 137 batters over 58+1⁄3 innings and was named the Illinois Gatorade Player of the Year.[5][6] He committed to play college baseball at the University of Notre Dame.[7][8]
Murphy made his professional debut with the Florida Complex League Braves and he also played with the Augusta GreenJackets. Over 12 innings, he gave up six earned runs. To open the 2023 season, he returned to Augusta and was promoted to the Rome Braves in August.[12] Over 21 starts between the two teams, Murphy went 6-4 with a 4.72 ERA and 113 strikeouts over 89+2⁄3 innings.[13]
Murphy began the 2024 campaign with the High–A Rome Emperors, compiling a 4–2 record and 1.54 ERA with 60 strikeouts across 7 starts. On May 29, 2024, it was announced that Murphy would require Tommy John surgery, ending his season.[14]