Tlustý was assigned to Sault Ste. Marie of the Ontario Hockey League (OHL) for the 2006–07 season, the holders of his major junior playing rights. In Tlustý's first 13 games of his OHL career, he sustained a high-ankle sprain that kept him out of the lineup for nearly six weeks as he attended treatment in Toronto. The injury also kept him from joining the Czech junior team at the 2007 World Junior Championships after initially being named to the pre-tournament roster.