The suspension begins with Charlotte's game Wednesday against the New York Knicks and will continue until Monk is determined to be in full compliance with the program.
The league announced the suspension Wednesday but did not disclose details of Monk's violation.
The third-year reserve from Kentucky is averaging 10.3 points and 2.9 rebounds in 21 minutes per game this season. However, he had been playing much better of late, averaging 18.2 points per game in his past seven games.
Monk has played in 191 games in his career, with one start.
Hornets coach James Borrego said before the game that he hadn't spoken with Monk since learning of the suspension.
"Obviously, we give him our full support," Borrego said. "It's a situation that -- all of us face different things in life. It's how you respond. It's my belief, knowing Malik, that he will respond the right way, and he has my full support, he has our organization's full support. And it does put us in a bind, but I believe that in the end, it's going to be a very positive story. I look forward to talking to him, but that's where we're at today."
The Associated Press contributed to this report.