Walker had surgery on Wednesday in New York, the team said.
If Walker returns in six weeks, he'd be back on the court March 11. That's more than a month before the NBA playoffs start on April 18.
The Hornets have the eighth-best record in the Eastern Conference entering Wednesday night's game against the San Antonio Spurs.
Without Walker, it makes the task of reaching the playoffs more difficult. Walker leads the Hornets in points (18.8), assists (5.2) and steals (1.4).
Coach Steve Clifford said after Monday's practice it would be a "significant hit" to the Hornets if Walker was out any length of time.
"He's been by far our best player," Clifford said. "You see it every year, every team. The Cavs without LeBron (James). Oklahoma City without (Kevin) Durant. ... It always starts at the top of your roster and that's why most teams that are winning have a superstar. He is playing at a real high level."
Brian Roberts will start in Walker's spot.
The 6-foot-1 Walker missed three of the last five games because of the knee injury.