Arsenal striker Welbeck limped off during England's 4-0 win over Lithuania at Wembley on Friday with a knee problem after scoring his sixth goal in five Euro 2016 qualifiers.
Liverpool forward Raheem Sterling and Manchester City midfielder James Milner are out with toe and knee injuries respectively, while Everton left-back Leighton Baines will also miss the trip.
Southampton defender Ryan Bertrand has been called up to the squad, leaving England with 17 outfield players on duty.
England head coach Roy Hodgson said: "We knew we were going to be losing Raheem Sterling who had an injection for an ongoing injury."