Crain was scheduled to begin pitching for Team Canada this week, but he felt a twinge in the groin area in his only outing of the spring on Feb. 25.
Crain, who posted a 2.44 ERA in 51 games for the White Sox last season, pitched for Team Canada in the two previous WBC events in 2006 and 2009. He plans to get treatment and rest for a couple of days before throwing again.
"Hopefully I will be able to throw again at the end of the week and start throwing hard again and off the mound by this weekend or early next week," Crain said.
Crain had an injury-plagued 2012 season, landing on the disabled list twice. He missed three weeks with a strained left oblique in April, then suffered a right shoulder strain, missing almost a month later in the summer. Crain also missed 10 days of spring training in 2012 with a right oblique strain.
The White Sox will take a cautious approaching in bringing Crain back.
"We have the best in the business (Sox training staff) taking care of him," Sox pitching coach Don Cooper said. "Jesse is smart enough to tell us when something isn't feeling right. We have plenty of time to get him right. I am not overly concerned as we speak."