Beckett, 33, has been out since May 14 with a groin injury but started to feel tingling in his fingers when was put on a throwing program. Beckett is 0-5 this season with a 5.19 ERA and 1.50 WHIP in 43.1 innings.
"Any time something like that happens to your arm or you start losing feeling and stuff, you think about it for sure," Beckett said last week. "I don't really want to think like that right now. I want to think about figuring out a way to deal with this."
The Dodgers come into Tuesday's action 24-32, good for last place in the National League West, seven and a half games back of the Arizona Diamondbacks.
The team still has no idea when Beckett will return, but they don't sound optimistic about his chances of coming back anytime soon.
"I don't feel like it's around the corner," manager Don Mattingly said.