The damage was revealed during an MRI on Wednesday morning.
The 36-year-old Eischen has been plagued by arm problems all season, and tried to pitch through them.
In his latest outing Monday night at Philadelphia, he threw to only two batters in the seventh inning -- walking both -- before leaving with shoulder pain.
"That just shows you what kind of heart this guy's got," Manager Frank Robinson told The Washington Post. "This is about the stage of his career when you don't know if it's the end of it."
This season, Eischen was 0-1 with an ERA of 8.59 in 14 2/3 innings (22 relief appearances). He has been a middle reliever his entire 10-year career, and has an 11-9 lifetime record, giving up 148 runs in 296 1/3 innings.
UPI horse racing weekend preview
Bo Jackson: I can't help Jameis Winston anymore