The crack was discovered Monday night after he was in Edmonton. Modano tried to skate with the injury Tuesday, but had to come off the ice after 15-20 minutes.
Modano told the media after the skate that he will be out at least a week.
"They found a little crack in it last night late after I got here, so there's not much movement I can do," Modano told The Dallas Morning News. "It started feeling pretty good [before the skate], but once I got on the ice and started moving around, it didn't feel too good. ...
"We're probably looking at a little while because everything we do seems to be connected to the ribs -- skating and shooting and everything we've got to do on the ice."
Richard Durrett is a reporter for ESPNDallas.com.