Van Persie will need more time to recover after picking up a thigh problem during the Carling Cup semi-final first leg against Tottenham.
Johan Djourou has been ruled out with a groin problem, leaving Arsenal short of cover in the centre of defence.
"I believe Tomas Rosicky will be okay to come back - but Johan Djourou is out as well. He has had an inflammation of his groin and in the next two weeks he will not be capable to play."
Dutchman van Persie, 24, has endured an injury-plagued season, suffering a knee problem earlier in the campaign, managing only 14 appearances, but netting seven goals.