Alfaro, who turned 22 on Thursday, had played in 49 games for Double-A Frisco and hit .253 with five home runs and 51 RBIs. He had a .314 on-base percentage and a .432 slugging percentage.
This is the third time in four seasons that Alfaro has had a significant injury. He missed two months in 2012 with a strained hamstring and one month in 2013 with a fracture in his left hand.
"Last year was the first year he played an entire year without getting hurt," Rangers catching instructor Hector Ortiz said. "This year we were hoping for the same thing. I feel for the kid. Every time he gets hurt, it's something bad. It's never minor."
T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, follow him on Twitter @Sullivan_Ranger and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.