Smith, 27, averaged 18.1 points and 5.3 rebounds a game while coming off the bench in all 80 games he appeared in this season.
Smith is in his ninth season in the NBA and led all non-starters in scoring average and 30-point games (seven). He was second on the Knicks only to Carmello Anthony in scoring average this season.
He helped New York to a 54-28 record and No. 2-seed in the Eastern Conference playoffs.
Smith was listed first on 72 of the 121 ballots and totaled 484 points. Los Angeles Clippers guard Jamal Crawford, with 31 first-place mentions and 352 points, was second and Golden State guard Jarrett Jack was third with 14 first-place votes and 170 points.
The award is determined in a vote by writers and broadcasters who regularly cover the NBA.