Dutch striker will be out for six weeks after damaging right ankle ligaments, Arsenal confirmed on Monday.
Van Persie was carried off on a stretcher early in the Netherlands friendly against Italy on Saturday after landing badly following a tackle by Giorgio Chiellini and there were initial fears that he could be out for several months.
However, Arsenal said the Dutch FA's assessment that the ligaments were only partially ruptured was correct.
Following the care given to Van Persie by the Dutch FA, he will travel back to London this week and continue his treatment with the Arsenal medical team at London Colney," a statement on Arsenal's website said.
"Van Persie will be out of action for approximately six weeks. We wish Robin a speedy recovery and look forward to seeing him playing again soon."
While the prognosis will be a relief to Arsenal manager Arsene Wenger it is still a blow to the north London club who are second in the Premier League table behind Chelsea.
The 26-year-old has thrived this season, scoring eight goals in his last 11 matches.
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