The league announced the suspension Wednesday but didn't disclose details of Monk's violation of the drug policy.
Monk's open-ended ban will start with Wednesday night's game between the Hornets and the New York Knicks, and will "continue until he is determined to be in full compliance with the NBA/NBPA Anti-Drug Program."
"We are disappointed in Malik's decision-making that resulted in his suspension," the Hornets said in a statement. "As an organization, we do not condone his behavior. However, we are committed to supporting Malik during this time."
Entering the Hornets' matchup against the Indiana Pacers on Tuesday, Monk was averaging a career-high 17.8 points per game since Jan. 24.
Monk, 22, has averaged 10.3 points, 2.9 rebounds and 2.1 assists in 55 regular-season games (one start) this season. The third-year reserve out of Kentucky has played in 191 games during his NBA career, averaging 8.6 points per game on 39.5 percent shooting from the field.