Delfouneso, who has provided back-up for Darren Bent, Emile Heskey and Andy Weimann, suffered the injury during the win over Iceland last week.
Villa boss Alex McLeish confirmed: "Nathan picked up a wee hamstring injury with England and it will probably keep him out of the weekend game."
He added: "We don't think it is too bad, a grade one tear, which usually leads to a quick recovery.
"It is a shame because he is one of the young boys vying for a place and his pace can cause real problems. The Man City game could have been one for him."