The Pirates announced the diagnosis on Monday and said the 38-year-old received a platelet-rich plasma injection.
The right-hander was placed on the disabled list Friday after complaining of right elbow soreness after allowing seven earned runs in a 15-5 loss at Cincinnati on Thursday.
“It is difficult,” Burnett said Friday. “I’m prepared for (anything) … if I just need some rest or something more. In my mind, surgery is not an option.”
Burnett is 8-5 with a 3.06 ERA this season in 21 starts.