"It didn't get tight on me, it didn't get stiff last night -- in fact, it felt really good," Cook said Sunday. "All things considered, it was successful."
Melvin would like to have him back on the big league roster following an off-day Monday.
"Good chance that he travels tomorrow and we activate him on Tuesday," Melvin said before Sunday's game. "Nothing's for sure yet, but that's the plan at this point."
Cook also missed the first week of the 2014 season with shoulder inflammation. The 2012 All-Star has a 2.92 ERA in 12 appearances this year.
Aaron Leibowitz is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.