Van Persie has yet to play during pre-season amid speculation over his future, as Manchester United, Juventus and Manchester City all try to sign the Dutchman.
Van Gaal said that he spoke to van Persie before calling him up for Holland's friendly against Belgium in midweek.
He said: "Robin will play his first game this Sunday. He has told me he is at least going to play 45 minutes this weekend.
"It is a good job, because I almost had not selected him."
Van Persie will play in Arsenal's final pre-season friendly against FC Cologne on Sunday, August 12.