Headrick did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[2] In 2021, he spent the majority of the year with the Single–A Fort Myers Mighty Mussels, also making a single start for the rookie–level Florida Complex League Twins. In 15 games (14 starts) for Fort Myers, Headrick logged a 3.82 ERA with 86 strikeouts in 61+1⁄3 innings pitched.[3] In 2022, Headrick made 25 appearances (23 starts) split between the High–A Cedar Rapids Kernels and the Double–A Wichita Wind Surge. In 108+1⁄3 innings of work, he posted a 10–5 record and 3.32 ERA with 136 strikeouts.[4]
On November 15, 2022, the Twins added Headrick to their 40-man roster to protect him from the Rule 5 draft.[5] Headrick was optioned to the Triple-A St. Paul Saints to begin the 2023 season.[6] On April 16, 2023, Headrick was recalled and promoted to the major leagues for the first time.[7] He made his MLB debut on April 19, earning the save.[8] In 14 games for Minnesota, Headrick posted a 6.31 ERA with 30 strikeouts across 25+2⁄3 innings pitched.
Headrick was again optioned to Triple–A St. Paul to begin the 2024 season.[9]