Van Persie doubtful for Dutch qualifiers
Van Persie was substituted in Arsenal's 2-1 win at Blackburn Rovers after injuring his ankle in a tackle.
"He twisted his ankle and the first news is 10 days (off)," said Arsenal manager Arsene Wenger. "If there is no bad news on Sunday it could be two weeks."
Van Persie missed a large chunk of last season through injury but recovered in time to help his country to the World Cup final in July.
Netherlands play San Marino on Friday before a home game against Finland the following Tuesday.