Kyle Walker and Aaron Lennon were hurt Sunday in Tottenham's match at Manchester City as was Jermain Defoe, whom England coach Roy Hodgson had wanted to call up as Rooney's replacement.
The fifth player forced out is Liverpool midfielder Jonjo Shelvey after he missed Sunday's match at Chelsea.
Coming into the squad are Tottenham midfielder Tom Huddlestone, who made the last of his three appearances in 2010, and 20-year-old newcomers Zaha and Carl Jenkinson.
Zaha is a highly rated forward with second-tier club Crystal Palace who has only made five appearances for England's under-21 team.
Jenkinson, an Arsenal defender, will be receiving FIFA clearance to play after previously featuring for Finland's under-19 team.
"It is expected that the paperwork will be completed and sent through to The FA on Monday, meaning Jenkinson will be available for the match with Sweden," the Football Association said.