Kashket, 20, joined the League Two club in August on a deal until January, but he has registered nine goals in four matches, including a hat-trick in the 5-0 triumph over Chesterfield in the second round of the FA Cup.
Wycombe manager Gareth Ainsworth said: "We gave Scott the opportunity to prove himself by giving him a deal until Christmas, and to say he has exceeded our expectations is an understatement.
"It was important for us not to miss out on the chance to extend his stay here as I’m sure there will be a lot of interest in him, and we have pushed really hard to get this deal done."