The right-hander had the surgery at Allegheny General Hospital.
After alerting the team's medical staff of an abnormality, Taillon consulted with Dr. John C. Lyne over the weekend. Lyne performed the surgery.
The recommended treatment plan for Taillon is pending further testing.
Taillon issued a statement on Twitter listing obstacles he has overcome.
"They have all just added fuel to my burning fire, and inspired me to become even better," he wrote.
Taillon remains on the 10-day disabled list.
Information from The Associated Press was used in this report.