Manager Joe Girardi said that Heathcott's injury came after he collided with outfielder Ronnier Mustelier in Thursday's 1-0 loss to the Blue Jays at George M. Steinbrenner Field.
Heathcott's MRI came back clean, according to Girardi, and he will be re-evaluated in the next few days.
The Yankees have been moving slowly with Logan, who made a career-high 80 appearances last season. Girardi said that Logan had a spot of discomfort in the back of his elbow and had to be scratched from a batting practice session on Friday.
"Boonie was doing good, and his elbow came up a little tender," Girardi said. "His MRI came up clean, so we'll probably just rest him a few days and get him back on the bump."