The Republic of Ireland international, 27, suffered medial ligament damage in training on Thursday.
Meyler has played 28 times for the Tigers in all competitions this season but has been an unused substitute in their last four outings.
Marco Silva's side sit two points above the Premier League relegation zone before Saturday's trip to Stoke City.
Hull City midfielder David Meyler will miss the remainder of the season after sustaining a knee injury.