Robin injured his ankle against Blackburn on August 28 and is set to be ruled out until the middle of next month.
The news on Van Persie will compound Arsene Wenger's frustration with Nicklas Bendtner also out with a groin injury.
The good news is that Samir Nasri is recovering well from knee surgery.
Nasri is ahead of schedule in his recovery from knee surgery after the Frenchman sustained a meniscal injury against Liverpool on the opening day of the season.
The 23-year-old was expected to be sidelined for a month but Nasri will return to full training in the next few days.
Source: Team Talk