Glasnow felt some discomfort throwing from 90 feet in Oakland on Sunday, and an MRI revealed inflammation. He will be reevaluated in three weeks with an aim to return in late August.
The 25-year-old led the major leagues with six wins and a 1.86 ERA when he was injured in early May. He was initially slated to return sometime around the All-Star break.
Meanwhile, Daniel Robertson had surgery to remove a loose body in his right knee on Monday and will also likely be sidelined until August.
Reliever Diego Castillo will miss about two weeks after the team placed him on the 10-day injured list with inflammation in his right shoulder on Sunday.