The 27-year-old was replaced at half-time of the Euro 2012 qualifier with Hungary in Amsterdam, after being floored by a tackle from Vilmos Vanczak.
Bert van Marwijk, the Holland coach, said of Van Persie's hopes of making an immediate return: "With luck he could play for Arsenal this weekend. Robin got a knee to his thigh. It didn't look very serious but it was too painful for him to carry on as he was hit by a knee above his own knee."
Van Persie was on Wednesday assessed by the club's medical team and the seriousness of the injury will become clearer over the next 24 hours.
Nicklas Bendtner returned from international duty having injured an ankle playing for Denmark but there is also optimism at the club that the striker will be fit for selection at the weekend, alongside the left-back Kieran Gibbs, who on Monday returned early from England Under-21 duty due to a groin injury.
Cesc Fábregas, Theo Walcott, Abou Diaby and Alex Song could all return to face Blackburn, although Johan Djourou, Thomas Vermaelen and the goalkeepers Wojciech Szczesny and Lukasz Fabianski remain on the injured list. Fábregas, who injured a hamstring in the Champions League defeat by Barcelona earlier this month, and Walcott, who last played in February, are believed to have trained well during the international break.
Arsène Wenger, the Arsenal manager, must also decide whether to stick with Manuel Almunia in goal or select Jens Lehmann for the first time since 2008. The 41-year-old played for Arsenal's reserve side in a 2-1 defeat by Wigan Athletic on Tuesday and declared the experience a qualified success.
"It was very beneficial for me to play a game," he said. "It is always good to learn a little bit what I could have done better. There are some situations that you can't play in a training game because in a real game there is a referee, linesmen. It was a good experience."
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