The team made the announcement Tuesday, saying Monk suffered the injury during a draft workout. He is expected to be sidelined for two to four weeks.
The Hornets expect Monk to be ready for training camp before the start of the regular season.
The 6-foot-3 Monk was selected 11th overall by the Hornets in last week's NBA draft.
Monk was named SEC freshman of the year after averaging 19.8 points per game for Kentucky. He shot 39.7 percent from 3-point range while earning a reputation as an outstanding midrange shooter.
He was the winner of the Jerry West Award given to the nation's top shooting guard after establishing a Kentucky freshman-record with 754 points. Monk finished as the second highest-scoring freshman in the country, behind only No. 1 pick Markelle Fultz (23.2 PPG for Washington).
The Associated Press contributed to this report.