Kennedy said he didn't feel anything from the strain during the throwing session, and he's been relatively pain-free since Thursday.
"Thursday, I felt a little something there because that was our first day of really stretching it out, trying to rub things out," Kennedy said. "On Friday, it felt significantly better. Saturday, it felt really good, and Sunday even better."
While the Yankees finished their road trip, Kennedy came back to New York after the injury to start the rehabilitation process. As far as a timetable for his return to the mound, Kennedy said he doesn't have any idea when he might be back.
"I just know I'll throw and play catch tomorrow, and hopefully the next thing after that is long toss."
The plan is to progress from light tosses and work his way back up to power pitches. But that doesn't mean it's easy for the young pitcher to tone it down.
"Today, I probably threw a little harder than I should have, but they said light toss," Kennedy said. "I mean, it's really hard to throw light."
Samantha Newman is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.