Henn, who turns 27 next month, has been limited to just three Grapefruit League appearances this spring due to what he called soreness in his pitching shoulder, though he did pitch in a Minor League game for New York on Wednesday.
"Hopefully, it won't be a long, drawn out process," Cashman said.
Envisioned as a frontrunner to serve in New York's bullpen as Joe Girardi's left-handed specialist, Henn has been bypassed by spring invitee Billy Traber, who was added to the Yankees' 40-man roster and recorded another two outs against the Phillies to drop his ERA to 1.08.
Cashman said that he did not know when Henn would begin a rehabilitation assignment, though he would remain behind in Extended Spring Training. Henn is out of Minor League options.
"I still have to pitch somewhere, whether it's here or with another team," Henn said earlier this week. "There's a window open here, but it's no secret I'm out of options. If I can get on the mound, it's only going to help my chances, no matter where I pitch."
In 29 appearances last season with New York -- including a start in the Yankees' final game of the regular season at Baltimore -- Henn was 2-2 with a 7.12 ERA. In 36 2/3 innings, he allowed 44 hits and 29 earned runs, walking 27 and striking out 28.
The Yankees made an additional roster move on Wednesday, releasing infielder Chris Woodward. The 31-year-old Woodward was a non-roster invitee vying to make the club as a utility infielder. He batted .393 with two RBIs in 15 Grapefruit League games but was slowed during camp by a tight right hamstring.
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.