Van Persie scored the winner the last time United beat City -- a 3-2 away victory in December 2012.
The Netherlands international has returned to training after suffering an ankle injury in United's defeat by Swansea City in February, but Van Gaal said the game against City at Old Trafford had come too soon for his compatriot.
"Van Persie is not fit enough to play," the Dutchman told a news conference.
"I don't think (defender) Luke Shaw is fit enough to play. But I cannot say they are not fit. In my opinion, they are not fit to play."
United's recent fine form -- they have won their last five Premier League games -- has lifted them to third in the table, eight points behind leaders Chelsea but one ahead of City.
Van Gaal has found success by using Wayne Rooney further forward, Juan Mata on the right, and Marouane Fellaini as a deep-lying target man, anchored by a midfield combination of Michael Carrick and Ander Herrera.
But Van Gaal, asked whether club record signing Angel Di Maria had done enough to force his way into the team against City, said he was not afraid to tinker with his line-up.
"'Never change a winning team' is an English expression, but I always have my eyes open," he said.
"It's also an obligation to the substitutes that you have, to compare players. You have to see also the quality of your opponent and you make a decision with the staff I have.
"Not only Angel (is pushing for a starting place), but every player who is training in the first squad are pushing because they want to do their utmost.
"I played 11 v 11 today (in training) and the team in white was very good -- the white team was not the basic line-up, so they are pushing always, and I like that. I said that to all of them, that I like the fighting spirit of every one of them."
(Writing by Stephen Wood, editing by Ed Osmond)
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