Muñoz signed with the San Diego Padres as an international free agent on July 7, 2015, receiving a $700,000 bonus.

[4] Muñoz started 2018 with Tri-City and was promoted to the San Antonio Missions of the Double-A Texas League in late June.

[3][6][7] Muñoz began the 2019 season back in the Texas League, with the Amarillo Sod Poodles,[8] going 0–2 with a 2.16 ERA, 34 strikeouts, and 11 walks over 16+2⁄3 innings.

[10] He made his major league debut that night against the Atlanta Braves, striking out one batter and walking one in one inning, with his fastball topping out at 101.9 miles per hour.

[11] Muñoz earned his first career MLB save on August 29,[12] allowing an RBI double to his future bullpen coach Stephen Vogt in the ninth inning of a 5–3 win over the San Francisco Giants.

[21] The contract included three additional team options for up to $24 million and bonuses for Muñoz based on the number of games he finishes.

[1] Muñoz returned to a setup role in 2022, working with several other relievers generally ahead of closer Paul Sewald.

He pitched 2+2⁄3 scoreless innings against the Toronto Blue Jays in the Wild Card Series, picking up the series-clinching win in Game 2.

[31] Muñoz did not allow a hit in 12 consecutive appearances, from July 5 to August 14, breaking a franchise record[32] and yielding no runs during that streak.