The 27-year-old Whelan was in line to make his Major League debut heading into Friday's series opener. He was 1-1 with a 1.67 ERA in 25 appearances at Triple-A this season, leading the International League with 18 saves.
His big league debut was marked by wildness: Pitching with a nine-run lead in the eighth inning of New York's eventual 11-7 victory over the Indians, Whelan walked four and recorded just two outs before being relieved, having issued a bases-loaded walk to rookie Cord Phelps.
"I said, 'We've all been through that first moment, the first time that we're on a big league field,'" manager Joe Girardi said. "There are a lot of nerves there, and you're never sure how you're going to react. The sun comes up the next day. We're not going to judge [him] too quickly on a first appearance."
In the Minors, Whelan had not allowed a run over his last seven outings, dating back to May 23. He was signed to a big league contract on Friday, with New York transferring right-hander Joba Chamberlain to the 60-day disabled list.
Whelan was acquired by the Yankees from the Tigers in November 2006 as part of a three-player package for outfielder Gary Sheffield.
Dickerson, 29, hit .357 (5-for-14) with three RBIs after being called up from Triple-A on May 17.