The Chicago White Sox selected Henzman in the fourth round, with the 117th overall selection, of the 2017 MLB draft.[7] Henzman signed with the White Sox. Since turning professional, he has been utilized primarily as a starter rather than as a reliever.[8] He made his professional debut with the Arizona League White Sox. After one scoreless appearance, he was promoted to the Great Falls Voyagers and spent the remainder of the season there, going 0–3 with a 4.00 ERA in 27 innings.[9] In 2018, he opened the season pitching for the Kannapolis Intimidators of the Single–ASouth Atlantic League[10] and was then promoted to the Winston-Salem Dash of the High–A Carolina League.[11] In 27 games (22 starts) between the two clubs, he pitched to a 6–4 record with a 2.35 ERA.[12] Henzman returned to Winston-Salem to begin 2019. After pitching in nine games for Winston-Salem, he was promoted to the Birmingham Barons. Over 24 starts between the two clubs, he went 7–8 with a 5.24 ERA.[13] On May 17, 2023, Henzman was released by the White Sox.
On February 22, 2024, Henzman signed a minor league contract with the Miami Marlins.[14] He made 12 appearances for the Double–A Pensacola Blue Wahoos, accompanied by a single scoreless outing for the Triple–A Jacksonville Jumbo Shrimp. In his time with Pensacola, Henzman compiled a 6.08 ERA with 10 strikeouts and one save across 13+1⁄3 innings of work. He was released by the Marlins organization on May 27.[15]
Baltimore Orioles
On June 4, 2024, Henzman signed a minor league contract with the Baltimore Orioles.[16] In 16 appearances for the Double–A Bowie Baysox, he posted a 4–2 record and 3.81 ERA with 25 strikeouts across 26 innings of work. Henzman was released by the Orioles organization on August 11.[17]
Oakland Athletics
On August 22, 2024, Henzman signed a minor league contract with the Oakland Athletics.[18] In 6 appearances for the Double-A Midland RockHounds, he posted an 0–1 record and 5.40 ERA with 3 strikeouts across 6+2⁄3 innings pitched. Henzman elected free agency following the season on November 4.[19]