McRae was averaging 12.8 points, 3.6 rebounds and 2.8 assists for the Wizards this season. The 28-year-old out of Tennessee had surgery on his right ring finger in October. He's recently been dealing with a twisted left ankle.
McRae joins a Nuggets team that's off to a 36-16 start and currently sits in third place in the Western Conference. He provides back-court depth behind Jamal Murray, Will Barton, Gary Harris and Monte Morris.
Napier, a 2014 first-round pick by the Hornets, was part of the four-team, 12-player trade on Tuesday, going from Minnesota to Denver.
He is averaging 9.6 points, 3.1 rebounds and 5.2 assists this season.
The Associated Press contributed to this report.