Van Persie was sent off for "serious foul play" by the referee, Grzegorz Gilewski, after he caught Alen Orman's face with a raised boot.
Orman had seven stitches and his team-mate Ljubo Milicevic said: "It was pretty brutal. Bruce Lee would have been proud of it."
On Thursday a Uefa spokesman insisted Van Persie would receive a two-match ban but, after receiving the referee's report, Uefa's control and disciplinary committee decided one match was sufficient. He will miss the trip to Ajax on 27 September.
"While Van Persie could reasonably be presumed to have had no intent to bodily harm his opponent," said a Uefa statement, "the reckless element involved in the challenge was punishable."
Arsène Wenger, the Arsenal manager, is still likely to ask the flying-phobic Dennis Bergkamp to travel to Amsterdam because Thierry Henry has a groin injury. Wenger is hoping to use that to his advantage by finding the opportunity to hold meaningful contract talks with his captain.
Wenger, who has already set a deadline of New Year's Day to reach an agreement, said: "I'm convinced he will stay here. He's not a guy who's obsessed by money."
- More about:
- Robin Van Persie