Damon sprained the shoulder when he ran into the left-field fence while attempting to catch a ball on July 4.
"Had a little tough time sleeping last night," Damon said after undergoing treatment Monday at the Yankees' minor league complex. "Today it felt a little sore. We're just going to hold back the swinging at least two more days. Hopefully it won't be too long of a time."
Damon, who is hitting .319, is on the disabled list for the first time in his career.
Yankees outfielder-designated hitter Hideki Matsui worked out strictly indoors Monday after taking batting practice on the field the previous two days.
"I think everything is progressing as planned," Matsui said through a translator. "Today I kept the workout and everything light. So far, everything is progressing."
There is no date yet for when Matsui will start a running program, a key step before he can play in minor league rehab games.
"Running, we don't know right now," Matsui said.
Also, Phil Hughes, coming back from a broken rib, threw 25 fastballs during his second bullpen session. He also threw 10 curveballs from halfway up the mound.
Relief pitcher Brian Bruney (foot) started a rehab game for Double-A Trenton, allowing one hit in a scoreless inning against Binghamton. He threw 15 pitches.
Left-hander Eric Milton, recently signed to a minor league contract, is scheduled for his first bullpen session Tuesday. He had elbow ligament replacement surgery in June 2007.