Vargas will miss at least two turns of the rotation but, if all goes well, he might return as soon as next Sunday against the Indians.
"That's the best case," Yost said. "Again, we've got to monitor him day to day and just see."
Vargas' fill-in, lefty Bruce Chen, is rooting for him.
"He's a strong guy and he works very hard," Chen said. "I saw him during the All-Star break and he was getting treatment, and was working on his stuff. He's a very good pitcher and we need him."
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.