The Rangers sent back minor-league forward Benn Ferriero and a sixth-round pick in the 2014 draft in the deal.
Falk registered three assists and 40 penalty minutes in 36 games for the Wild last season.
The draft-day deal will likely be the only one for the Rangers, despite some big names surfacing in recent trade discussion. With the team's decision to not buy out Brad Richards, it has little maneuverability under the cap to make any splashy moves.
The Rangers do not have a pick until the third round of the 2013 draft.