The corresponding fixture last season was marred by instances of disorder, which included United defender Rio Ferdinand being hit by a coin.
Hart himself also grabbed a supporter who ran onto the pitch.
In a message to City fans via the club's official website, Hart said: "The derby is one of the most anticipated and exciting games in world football.
"As players, we are all looking forward to Sunday, and we know that the fans will be too.
"The home support is so important for us, and I know they will be like an extra man for the team on the day.
"As always, we need our fans in full voice, but we also need them to respect the occasion.
"We want everyone to enjoy the game but be sensible too.
"There were incidents last year which no-one wants to see repeated.
"The eyes of the world will be on this game as usual, and I'm confident our supporters will do the club proud.
"Our fans are the best in the world and we want you to show your passion for the club, but in the right way."
Greater Manchester Police announced earlier this month they would be stepping up security procedures around the fixture.