Manager Paul Lambert told the club's official website: "Chris has been brilliant for us so far this season. He has been playing on top of his game and he deserves this new contract.
"It's great for the club to have players who have come through the Academy. He's still only 21 and is a terrific finisher with both feet, as he showed against Colchester last weekend."
Martin added: "I'm delighted to sign a new deal. This season has been very good for me and everybody connected with the club so far and hopefully we can carry that on."