Roy Hodgson takes his patched-up team to Donetsk to play their Group D opener against France on Monday and Arsenal boss Wenger fears the Three Lions may as well pack their bags and come home if they lose to Laurent Blanc's men.
He said: "The opening game is England v France and there is no Rooney. You would say that is a game that you can not afford to lose.
"Why? Not because you cannot catch up, but the pressure inside the country becomes tremendous straight away.
"That game could dictate the whole group. If it's a 0-0 draw, the group is all open, but if someone loses they have a very good chance of going out because Ukraine will beat one of the two, you would say, and Sweden are a hard team to beat.
"They are always well-organised tactically and they have Zlatan Ibrahimovic coming back, who can make a difference.
"They are traditionally a difficult opponent for England. It's a difficult group overall."