The 28-year-old Crotty, who was expected to be named in Steve Hansen's All Blacks squad for the three-test series on Thursday, suffered rib cartilage damage in the Crusaders' 25-22 win over the Highlanders on Saturday.
Initial assessments suggested he could be out for at least two weeks but the Crusaders' assistant coach Jason Ryan said they needed to check a scan before they could determine the extent of the injury.
"It will be a case-by-case thing," Ryan said. "Cartilages can be pretty niggly, especially when you are sneezing or coughing.