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The Cardiff Blues fly-half or full-back was nursing an ankle injury when Warren Gatland omitted him from Wales' initial 31-man squad.
Full-back Leigh Halfpenny (knee) is a doubt after coming off on a stretcher in their 23-19 win over Italy.
Anscombe was a candidate to be recalled if Halfpenny is ruled out.
New Blues coach Danny Wilson confirmed New Zealand-born, once-capped Anscombe will not play for at least two to three more weeks.
Wales' World Cup campaign kicks off against Uruguay on Sunday, 20 September.
Versatile Gloucester star James Hook, who has made 78 Wales appearances, is also a contender to be recalled should Toulon's Halfpenny's injury prevent him appearing at the tournament.
Before the Italy game, Gatland said Scarlets back-three star Liam Williams would take a full part in training next week.
Scarlet Williams has not played since having foot surgery in the summer and would be the leading candidate to take over from Halfpenny.
Matthew Morgan, of Bristol, and Newport Gwent Dragon Hallam Amos are also a back-up options already named in the squad as fly-half and wing respectively.
If Halfpenny is ruled out, Ospreys fly-half Dan Biggar is likely to take over the goal-kicking duties.
Gatland also has a major concern over scrum-half Rhys Webb, who was also taken off against Italy with what seemed a serious ankle injury.
Racing 92's Mike Phillips is most likely to earn a recall should Webb's absence be confirmed.
Wales' injury worries ahead of the 2015 World Cup have worsened with Gareth Anscombe ruled out for at least two weeks.