Wang's biceps felt tender when he played catch before Monday night's game against Baltimore and won't attempt to throw again until Friday.
"It's not exactly the news that I wanted," Yankees manager Joe Girardi said. "It's not what you want to hear because we were hoping that two weeks' rest is enough for him to get on a throwing program."
The 29-year-old right-hander has not appeared in a game since July 4, when he left a start against Toronto after 5 1/3 innings.
"We're going to give him a few more days and some more strengthening before he goes back out," Girardi said. "I think anytime you're dealing with cuff issues or shoulder tendinitis or whatever you want to describe it as, I mean, there's concern. And whatever he's able to do, we would love to have. But I think any time someone is injured and you're not sure when they're exactly going to be back, you can't really count on them in a sense."
Wang injured his right foot while running the bases at Houston on June 15 last year and missed the rest of the season. Hit hard at the start of this year, he didn't pitch for the Yankees from April 18 to May 22 because of what the team described as weakness in the adductor muscles in his hips
He is 1-6 with a 9.64 ERA, getting his first win of the year at the Mets on June 28. Alfredo Aceves made a spot start in his absence and Sergio Mitre is to take over as the No. 5 starter on Tuesday night against Baltimore.
"Sergio Mitre has a chance to step up and fill the void for us," Girardi said. "The key for him is his sinker. If his sinker is going, he's going to give us some distance."
New York doesn't want to shift Phil Hughes back to the rotation, saying it would take three to four weeks to get him back to 100 pitches. If another starter gets hurt after Damaso Marte returns, it likely would be Aceves moving from the bullpen.
Marte, on the disabled list since May 3 with weakness and tendinitis in his pitching shoulder, is to make an injury rehabilitation appearance Tuesday with Triple-A Scranton/Wilkes-Barre following two-inning outings Thursday and Saturday for the Gulf Coast Yankees.