The first Yorkshire derby of the season comes at Sheffield Wednesday on August 26, with the Owls making the return trip on March 3.
Leeds face a Boxing Day trip to Sunderland and host Coventry on New Year's Day.
Kevin Blackwell said in the Yorkshire Evening Post: "It's a good start for us against Norwich, and to be fair I think both sides are going to be contenders for promotion next season.
"The first two months are going to be a tough test and we've got some big games in there, but other teams will be looking at it and realising that they have to play Leeds United. We're never an easy game.
"It's as tough for them as is for us, and we'll go into the season with a lot of confidence."
The Whites meet all three of the clubs relegated from the Premiership last season, Sunderland, Birmingham and West Brom, before the end of September.