The Houston Astros selected Salazar in the seventh round, 222nd overall, of the 2018 MLB draft.[4] He spent his first professional season playing 36 games between the Low-A Tri-City ValleyCats and Single-A Quad Cities River Bandits. He spent the 2019 season with Quad Cities, hitting .262/.323/.371 with 3 home runs, 39 runs batted in (RBI), and 5 stolen bases across 71 games. Salazar did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[5]
Salazar spent the 2021 season split between the High-A Asheville Tourists and Double-A Corpus Christi Hooks, also appearing in one game for the Triple-A Sugar Land Skeeters. In 56 total games, Salazar hit a cumulative .251/.338/.492 with 11 home runs, 32 RBI, and 4 stolen bases. In 2022, he spent the majority of the year with Corpus Christi, ending the year with Sugar Land, who had rebranded as the Space Cowboys. In 102 games between the two affiliates, he slashed .265/.338/.445 with 16 home runs, 60 RBI, and 8 stolen bases.[6]
On March 28, 2023, the Astros announced that Salazar had made the Opening Dayroster.[7] He had his contract selected to the 40-man roster on March 30. On April 2, 2023, Salazar made his major league debut, appearing as a pinch hitter and drawing a base on balls (BB) in his lone plate appearance that game.[8] Salazar singled on April 16, for his first major league hit off of Josh Sborz in the ninth inning versus the Texas Rangers at Minute Maid Park.[9] Salazar saw sporadic playing time with Houston, going 2-for-14 with a walk in only 10 games. He was optioned to Triple–A Sugar Land on June 5, after the team promoted Grae Kessinger.[10]
Salazar was optioned to Triple–A Sugar Land to begin the 2024 season.[11] On June 19, 2024, Salazar drove in 2 runs with two hits for his first career multi-hit game in the majors to key a 4–1 win over the Chicago White Sox.[12] In 2024, he played 12 games for the Astros, batting .320/.387/.400 in 32 plate appearances, with 2 doubles, 5 runs scored and 8 RBI. He played 10 games as catcher.[13]