The Wild chose the six-foot-three defenceman from Savage with the 12th overall pick in the 2004 draft. He was coming off a stellar freshman season at Michigan State, where he was a second-team All-American.
But Thelen ran into trouble at the school and was kicked off the hockey team after being caught drinking underage.
He spent the next two years in the Western Hockey League, where he helped the Vancouver Giants win the Memorial Cup.
The Wild had until Friday to sign him to a deal or forfeit his rights. The Wild will receive the 42nd overall pick in July's draft as compensation.
The Wild also failed to get deals done with two 2005 draft picks - third-round goaltender Kristofer Westblom and fourth-round centre Kyle Bailey.