He was replaced on the roster by starting pitcher Chance Adams, who was recalled from Triple-A Scranton/Wilkes-Barre.
Chapman left Tuesday's 2-1 win over the Miami Marlins in the 12th inning after feeling pain in the knee.
Speaking through an interpreter, Chapman said Wednesday that he didn't know a set timeline on his return but that he at least wanted to use these 10 days to rest the knee.
"That's what you hope for, that it's only 10 days and you take this time, recuperate and get back to being 100 percent," Chapman said.
The pitcher will see a doctor in New York on Friday while the rest of the Yankees open a four-game series at Baltimore.
Manager Aaron Boone said the Yankees hope to have a more definitive understanding of a timeline for Chapman's recovery after he meets with the doctor.
"We've got to keep working on it," Chapman added. "We'll keep doing treatment and see how the knee reacts. We've got to let it rest -- fully rest -- and see how the knee reacts to [the time off]."
The Yankees are well-equipped to replace Chapman at the back end of the bullpen. David Robertson and Zach Britton each have saved more than 100 career games, and set-up man Dellin Betances has seen time at closer in past seasons.
Boone said he'll use a combination of all three pitchers going forward.
Chapman, who has pitched through knee problems for much of the season, departed after throwing just six pitches in Tuesday's relief appearance.
He said he felt some discomfort in the knee while warming up, but the pain worsened while he was in the game, prompting him to call for the trainers.
"Discomfort is constant when I'm pitching, and I use my legs, put my effort on my legs and knee, and then you feel it more," Chapman said.
Known to register triple digits on the radar gun, Chapman topped out at 97.1 mph in the six pitches he threw. Altogether, his pitches averaged 96 mph. Per ESPN Stats & Information research, that's his lowest average velocity in a game since 2013.
Boone said Wednesday that he believes Chapman will bounce back well after this DL stint.
"I'm confident that he's going to play a major factor for us down the stretch and in the postseason," Boone said. "I do think this is something that we'll be able to manage."