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.
"They can take a while to settle down, but I am not too sure."
The Lions face the Blues at Eden Park on Wednesday prior to the match against seven-times Super Rugby champion Crusaders on Saturday, with coach Scott Robertson able to select his All Blacks for the game before they head into camp.
Robertson had said last week it was likely they would field as close as possible to a full-strength side at Rugby League Park, but Ryan said they would also keep an eye on their All Blacks' workload, especially captain Sam Whitelock.
"Sammy is like the rest of them, he has got a few niggles," Ryan said. "We have to be smart there, there is a bigger picture for the All Blacks. We don't want to flog them.
"Steve (Hansen) and the All Blacks coaches will want them fresh for the series, so we want to give everyone an opportunity in the 23 to play against the Lions."