On December 12, 2013, Munson was selected by the Philadelphia Phillies with the fourth pick in the Rule 5 draft. According to the rules, Munson had to make the Phillies' Opening Day roster and remain with the team for the entire season, or the Phillies will have to offer Munson back to the Diamondbacks.[7] After competing for a spot in the Phillies' bullpen during spring training,[8] he was returned to the Diamondbacks on March 18, 2014.[9]
Munson pitched for Reno in 2014, compiling a 4–3 win–loss record with a 2.60 earned run average. After the season, the Diamondbacks added Munson to their 40-man roster to protect him from the next Rule 5 draft.[10] Munson pitched in 36 games split between the rookie–level Arizona League Diamondbacks, Double–A Mobile BayBears, and Triple–A Reno. The majority of his work came in Reno, where he posted a 4.45 ERA with 30 strikeouts and 2 saves in 32+1⁄3 innings of work. On August 31, 2015, Munson was designated for assignment after Phil Gosselin was activated from the injured list.[11] He elected free agency following the season on October 13.
Seattle Mariners
On July 1, 2016, Munson signed a minor league contract with the Seattle Mariners. In 19 appearances for the Triple–A Tacoma Rainiers, he recorded a 4.44 ERA with 28 strikeouts across 26+1⁄3 innings of work. Munson elected free agency following the season on November 7.[12]
Lancaster Barnstormers
On March 28, 2017, Munson signed with the Lancaster Barnstormers of the Atlantic League of Professional Baseball. He became a free agent after the 2017 season. Signed with the Tigres Del Licey, in the winter of 2017. Had a 3.12 ERA with 11 strikeouts in 8+2⁄3 innings pitched.
On February 19, 2018, Munson re-signed with the Lancaster Barnstormers.
[13] He became a free agent following the season.
On January 7, 2020, Munson signed a minor league contract with the Seattle Mariners. He did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[14] Munson became a free agent on November 2.[15]
On January 5, 2021, Munson re-signed with the Mariners organization on a minor league contract. On April 15, Munson was released by the Mariners.[16]