Rinne was drafted 258th overall in the eighth round of the 2004 NHL Entry Draft by the Nashville Predators. He was signed by the Predators on 23 August 2005, and began his North American playing career with the Predators' top minor league affiliate, the Milwaukee Admirals of the American Hockey League (AHL). Initially, Rinne was slated to be the backup for Brian Finley, but Rinne became the starter as a consequence of Finley's poor play. In the summer of 2006, Rinne was "roughed up by a couple of unknown assailants" and during the fight, he dislocated his shoulder. As a result, he had to have surgery and missed the first four months of the season.