He earned the 2012 Gatorade South Carolina Baseball Player of the Year and Region 8-2A Player of the Year in his senior season, after posting a 7–1 win–loss record with a 0.89 earned run average (ERA) and 111 strikeouts in 50 innings pitched to help his team reach the regional championship.

[2] The Boston Red Sox selected Callahan in the second round (87th overall) of the 2012 MLB Draft and he chose to forego his commitment to South Carolina in favor of a $565,500 signing bonus.

Callahan spent 2016 with the Salem Red Sox where he posted a 5–3 record and 3.29 ERA in 36 relief appearances, and he began 2017 with the Portland Sea Dogs.

On July 31, 2017, the New York Mets acquired Callahan, Stephen Nogosek, and Gerson Bautista in exchange for Addison Reed.

[8] On December 28, 2018, Callahan signed a minor league contract with the San Francisco Giants that included an invitation to spring training.

On April 26, 2022, Callahan signed with the Wild Health Genomes of the Atlantic League of Professional Baseball.