Hornacek said he believes the 32-year-old Anthony injured his knee while blocking a shot in the second half of the Knicks' 112-105 loss to the Golden State Warriors on Sunday.
Anthony scored 15 points on 6-for-12 shooting in 35 minutes. He scored just two points without taking a field goal in the fourth quarter.
Ron Baker will start in place of Anthony.
Anthony, a 10-time All-Star, is averaging 23.2 points, ranking him 17th in the NBA, as well as six rebounds and 2.9 assists this season.