The Pirates placed Rodriguez (elbow) on the 60-day injured list Wednesday.
The transaction is a procedural move to clear a spot on the 40-man roster for catcher Yasmani Grandal, whom the Pirates signed to a one-year contract. Grandal is projected to slot in as the primary backup to top catcher Henry Davis while Rodriguez is set to miss the entire 2024 season after undergoing surgery in December to repair the UCL and flexor tendon in his right elbow.