Carrick carried an Achilles injury into United's 1-0 win over Arsenal and even though he completed 90 minutes at Old Trafford he has withdrawn from the England squad.
Welbeck has not played since October 19 because of a knee injury and he has also pulled out of the double-header.
England's preparations for the matches received a slight disruption when they were forced to change their hotel because of a virus at St George's Park.
The squad met up in Watford on Tuesday, rather than their normal base in Staffordshire, although the FA insists this was a precautionary measure.
No England players are understood to have been affected by the virus.
Positive news for Hodgson is that captain Steven Gerrard (hip), Gerrard's Liverpool team-mate Daniel Sturridge (foot) and Arsenal midfielder Jack Wilshere (ankle) have joined up with the squad despite their respective injury problems.
The squad will train at Arsenal's base in London Colney on Tuesday afternoon and Wednesday before they host Chile at Wembley on Friday night.
Hodgson has always said he would use the two games as an opportunity to experiment with emerging players.
Welbeck's withdrawal also means Jay Rodriguez has a good chance of featuring against the South Americans, as Hodgson has already described the uncapped Southampton man as an ideal replacement for the Manchester United forward, who has been a regular under the current England boss.
Captain Gerrard has been troubled by a hip problem for the last couple of weeks and is expected to play just one of the two matches.
Frank Lampard, who will be awarded a commemorative 100th cap before the Chile game, may captain the side against Chile.
Lampard's two daughters, Luna and Isla, are understood to be mascots for the clash against the South Americans.
"The Manchester United duo featured in last month's World Cup qualifier against Poland, but are ruled out as Roy Hodgson's men gather for two games at Wembley Stadium.
"No additional players will be added to the squad of 26 players."
England will be looking to prove that they can cut it with the best next week when they play Germany at Wembley, but Friday's encounter with Chile in London also promises to be an intriguing encounter.
Chile qualified for the World Cup after finishing third in the fiercely competitive South American qualifying group and their squad contains highly-rated Barcelona forward Alexis Sanchez.
One problem facing the Chileans, who take on Brazil in Canada next week, is that Juventus midfielder Arturo Vidal is likely to miss the game at Wembley because of a thigh injury he suffered against Napoli at the weekend.
The 26-year-old will join up with the Chile squad in London on Tuesday afternoon, but Juventus expect him to miss the England friendly.
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- Roy Hodgson
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