Carrick played the entirety of United's 1-0 win over Arsenal on Sunday but has been carrying an Achilles injury, while Welbeck has not played since October 19 due to a knee complaint.
England manager Roy Hodgson has not called up any replacements, leaving him with a 26-man squad for Friday's game against Chile at Wembley Stadium and the match against Germany at the same venue next Tuesday.
The squad subsequently met up in Watford, north of London, and the FA has confirmed that they will train at Arsenal's London Colney training centre on Tuesday and Wednesday.
Revised England squad:
Goalkeepers: Fraser Forster (Celtic/SCO), Joe Hart (Manchester City), John Ruddy (Norwich City)
Defenders: Leighton Baines (Everton), Gary Cahill, Ashley Cole (both Chelsea), Kieran Gibbs (Arsenal), Phil Jagielka (Everton), Glen Johnson (Liverpool), Phil Jones, Chris Smalling (both Manchester United), Kyle Walker (Tottenham Hotspur)
Midfielders: Ross Barkley (Everton), Tom Cleverley (Manchester United), Steven Gerrard (capt), Jordan Henderson (both Liverpool), Adam Lallana (Southampton), Frank Lampard (Chelsea), James Milner (Manchester City), Andros Townsend (Tottenham Hotspur), Jack Wilshere (Arsenal)
Forwards: Jermain Defoe (Tottenham Hotspur), Rickie Lambert, Jay Rodriguez (both Southampton), Wayne Rooney (Manchester United), Daniel Sturridge (Liverpool)