The 25-year-old, who has scored six goals and four assists in 43 matches across all competitions this season, picked up the problem during Forest's Europa League quarter-final second-leg victory over Porto on Thursday.
"Nottingham Forest can confirm that Callum Hudson-Odoi suffered an injury to his right quadriceps muscle," the club said in a statement.
"Following further specialist consultation, the winger has undergone surgery today and will commence his rehabilitation with our medical staff immediately.
"Callum is expected to return to full training during the pre-season period, and everyone at the club wishes him a speedy recovery."
Forest are 16th in the Premier League with 36 points and five matches remaining. They are five points clear of 18th-placed Tottenham Hotspur in the relegation zone.