Dempster went on the disabled list with a sore right latissimus dorsi muscle. He hasn't pitched since June 15 and is 3-3 with a 2.11 ERA.
Chris Volstad was sent down to Triple-A Iowa in a corresponding move.
Dempster felt good after a bullpen session on Wednesday, and the 35-year-old veteran said the heat in New York will help him get loose.
The fact the game is the last before the All-Star break will give manager Dale Sveum the opportunity to keep Dempster on a low pitch count (between 70-80) and use the entire pitching staff to back him up out of the bullpen.
"He says he feels as good as he has all year," Sveum said before Friday's game. "It's just a matter of durability issues."
Dempster and team president Theo Epstein had a meeting on June 13 about Dempster's future with the team. Several teams have been scouting him, and Dempster is resigned to the fact he may be traded from the rebuilding Cubs. Dempster is in the final season of a four-year, $44 million deal that pays him $14 million in 2012.
"When you're young and get traded you see it as a negative sometimes, but if you look at it from the other side that means other teams are interested in you," Dempster said recently. "It's humbling, and you appreciate it. But at the same time it does not change anything that you do, that you go about your business and get ready to pitch."
The risk in pitching Dempster on Sunday is possibly aggravating the injury and affecting a possible trade scenario.
Dempster has 10 and 5 rights that allow him to veto a trade.
ESPNChicago.com's Bruce Levine and ESPNNewYork.com's Mike Mazzeo contributed to this report.