Rodriguez has been on the disabled list since June 6 with stiffness in his left forearm, though he was also found to have arthritis in his elbow when examined by orthopedist James Andrews last month.
"Wandy has worked diligently to return to action but despite all Wandy's and our medical staffs' work and efforts, he has not been able to return to pitch without pain," general manager Neal Huntington said in a statement. "We have decided that it is in Wandy's best interests and the Pirates' best interests to allow more time for the injury to the flexor tendon in his left forearm to heal and to shift our focus from a return in 2013 to having Wandy ready for Opening Day 2014."
The Pirates made the move Saturday.
Rodriguez made 12 starts for the Pirates this season, going 6-4 with a 3.59 ERA.
The 34-year-old Rodriguez can become a free agent at the end of the season but also holds a $14 million player option in his contract to return in 2014.
Information from The Associated Press was used in this report.