Edwards is highly regarded at the Premier League side, but Mauricio Pochettino has used the 19-year-old in his first-team squad on just one occasion.
However, the winger has been given the chance to continue his development at Carrow Road after being brought in by Canaries boss Daniel Farke.
The 41-year-old told the club's official website: "Marcus is a young player with huge potential. He is rated as one of the biggest talents in English football but will need some time to adapt to a new surrounding and to the physical game in the Championship.
"Again, it's a sign of our way to work with young and talented players."
Edwards is not eligible to feature for Norwich in their FA Cup third-round replay with Chelsea on Wednesday night.