The 30-year-old backstop hit .271 with three homers, three doubles and 17 RBI in 34 games with the Bucs before his setback.
Snyder has a $6.75 million option for 2012, but if the Pirates choose not to exercise it, he will become a free agent.
Also on Monday, starter Jeff Karstens will miss his next scheduled start, on Wednesday against Houston, due to lingering arm soreness and fatigue.
Pirates manager Clint Hurdle said that Brian Burres will take that spot in the rotation.
Karstens is 9-8 with a 3.32 earned run average in 28 games (24 starts) this year.