Yankees manager Girardi said the destination has not been picked, but that Triple-A Scranton/Wilkes Barre was the likely spot.
On Saturday, Kelley (3.52 ERA in 15 1/3 innings) logged two-thirds of an inning, walking one batter and striking out two in his first rehab stint since being placed on the 15-day disabled list on May 13.
"One outing to me is not a lot when you've been out a month, so we just felt for him that it'd be better to make sure he bounces back," Girardi said.
Girardi said the 20-pitch limit Kelley operated under on Saturday would likely remain on Monday.
Jackson Alexander is an associate reporter for MLB.com.