The move helps address a balance issue, with Laffey joining Boone Logan as the only two lefties in the bullpen.
"He's a guy that can give you some multiple innings, but he's another left-hander for us," Yankees manager Joe Girardi said. "That's why we went and got him."
Laffey went 1-1 with a 4.01 ERA in 42 2/3 innings for the Mariners this season. Girardi said Laffey can be used as a situational guy or a long reliever, but that Logan will remain the primary lefty late in games.
Garcia threw a bullpen session Sunday and said he felt good. But Girardi said the move is a precaution because Garcia has not pitched in two weeks.
"I don't think Freddy really wanted to go on [the DL]," Girardi said. "I think Freddy wanted to pitch Sunday but we just thought it was the safer route.
"When you're a starter, you're used to working every fifth or sixth day and he hasn't pitched in two weeks. We just thought it would make sense to see how he comes out after today's bullpen, have him throw on Monday somewhere and test the finger to make sure it's OK and just get sharp again."
Garcia will pitch for Triple-A Scranton/Wilkes-Barre on Monday. If all goes well, he will return to start one game of the doubleheader against Baltimore on Aug. 27.
Garcia said he threw all of his pitches in the bullpen session and would have preferred to make his scheduled start against Minnesota on Sunday.
"That's their decision, I don't have much to say," Garcia said. "I am fine, that's the decision they made."