Masset is available to pitch out of the bullpen in Monday night's game against the Texas Rangers.
The 31-year-old Masset has not pitched in the major leagues since 2011 when he was with Cincinnati. He has dealt with an injured right shoulder for the past two seasons.
The Rockies signed Masset to a minor league contract on Feb. 1. He made eight scoreless appearances in Triple-A this year.
In 308 career games with Texas, the Chicago White Sox and the Reds, Masset is 16-14 with four saves and a 3.78 ERA.
The Rockies selected Masset's contract from Triple-A and optioned Wheeler to Colorado Springs.
The team also transferred righty Tyler Chatwood from the 15-day disabled list to the 60-day DL with a strained right elbow.