The trade is part of a three-team deal that involves the Nuggets, Knicks and Dallas Mavericks.
New York will send Doug McDermott to Dallas.
Dallas will send point guard Devin Harris and a future second-round pick to Denver.
Mudiay was the seventh overall pick in the 2015 NBA Draft. After starting 107 games during his first two seasons, Mudiay has not started for the Nuggets this year, according to ESPN.