ESPN's Ian Begley noted the sprain looked severe and added Knox was disqualified for the remainder of the game for being unable to shoot free throws following the injury.
Shams Charania of The Athletic reported x-rays on Knox's ankle were negative.
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The rookie went down late in the first quarter while driving to the basket against Celtics guard Terry Rozier.
After one year at Kentucky, Knox declared for the NBA draft and became the Knicks' top pick at No. 9 overall. The 19-year-old averaged 15.6 points and 5.4 rebounds per game for the Wildcats and was named SEC Co-Freshman of the Year with teammate Shai Gilgeous-Alexander.
"Like Oubre, Knox is an exciting athlete who makes his mark by shooting, slashing and getting out on the break," Wasserman wrote.
Entering Saturday's contest, Knox was averaging 13.5 points and 3.0 rebounds in two games.
The Knicks are still trying to build a playoff-worthy roster in the Eastern Conference. Knox is a key piece of the future, and the team hopes he can develop into a strong No. 2 option behind the injured Kristaps Porzingis (torn ACL).
While it isn't yet known if Knox will miss significant time, Lance Thomas will likely continue to start at small forward, with Mario Hezonja also playing substantial minutes during Knox's potential absence.