While an exact timetable for Brito is unknown, manager Torey Lovullo said that Brito will be out at least two months.
Brito, the D-backs' No. 6 prospect per MLBPipeline.com, was competing with Gregor Blanco, Jeremy Hazelbaker and Reymond Fuentes to be the primary backup for A.J. Pollock in center.
"One of our top priorities was to find somebody who could help A.J., give him some time off," Lovullo said. "We still have some good candidates. Unfortunately, losing Socrates is one of those considerations that won't be around for a while."
Even with Brito's injury, Lovullo said that Chris Owings, who filled in for Pollock last year, will not see time in center if he plays the outfield, but rather will play right.
For now, Owings is playing mostly shortstop, as he competes with Nick Ahmed and Ketel Marte for the starting job.
Steve Gilbert has covered the D-backs for MLB.com since 2001. Follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.