Taillon, the No. 2 pick in the 2010 draft, pitched for the Curve in 2013 and went 4-7 with a 3.67 ERA.
"I've had an MRI, and the ligaments are all good," Taillon said. "There's nothing there, which is really good news. I'm going to go get a second opinion, and we'll go from there. The early word is just there's a little inflammation and a bone there in my elbow. Nothing too, too serious."
Taillon will seek a second opinion this week. In a text message, Taillon said he was not certain which doctor he'll see for the second examination.
Indianapolis will open its season April 3 at Columbus.