Kretzschmar becomes the fourth player to extend his stay at Adams Park recently, following in the footsteps of Matt Bloomfield, Dean Morgan and Lee Angol.
The 19-year-old attacking midfielder has been with Wanderers for five years and signed his first professional deal 12 months ago.
He told the club's official website: "I'm delighted to be staying. I've been here since I was 14 and it's a dream come true to sign a new contract.
"I've been in love with the club since the day I joined and I just want to keep it going.
"Seeing Josh (Scowen) play 30 or 40 games last season inspires you to do what he's doing, Jesse (Kewley-Graham) as well.
"Hopefully I can get on the bench a bit more, make my debut and get some appearances under my belt."