Although the Welsh Rugby Union have not ruled him out of the tournament, which kicks off in New Zealand on September 9, Henson faces a recovery period of six to eight weeks.
The 29-year-old went off during the first half of Saturday's 19-9 victory over England in Cardiff.
Even if he recovers in six weeks, Wales' pool campaign will be well under way by then. Coach Warren Gatland is due to name his 30-man World Cup squad on August 22.
If, as appears inevitable, Gatland does not name Henson in the original party, then he could only play a part in the competition by replacing an injured player.
Henson has never played in a World Cup, being overlooked by then Wales coach Steve Hansen in 2003, and failing to recover in time from injury four years later.
"Gavin underwent surgery this morning at the Vale Hospital to correct the dislocation to a bone in his right wrist," Prav Mathema, the WRU's national medical performance manager.
"He has been given a return to play time of six to eight weeks which, while ruling him out of selection for the initial World Cup squad, could see him available to the coaches while we are still in the pool stages of the tournament.
"With that fact in mind, Gavin will remain under the care of the Wales national squad medical staff in order to ensure that he returns to fitness at the earliest opportunity in case the coaches need to call him out to New Zealand for any reason."
Henson, who is currently without a club after spells at Saracens and Toulon last season, impressed during his 30 minutes on the pitch.
He had said beforehand he felt he needed to do something "pretty special" to make Gatland's squad, but injury has now dashed those hopes.
Henson's injury is the latest setback for Gatland ahead of a World Cup campaign that sees Wales grouped with South Africa, Samoa, Fiji and Namibia.
Scarlets wing Morgan Stoddart broke his leg against England at Twickenham eight days ago, while last season's Wales skipper - hooker Matthew Rees - is battling to overcome a neck problem.
With Henson sidelined, Gatland could thrust 20-year-old Scott Williams into his midfield plans, but Henson will be a significant loss, given his versatility as a centre, full-back or fly-half.
The injury is another career dip for Henson, who spent almost two years out of the sport as he came to terms with repeated injury blows.
During that time, he embarked on a television career, taking part in programmes such as the BBC's Strictly Come Dancing, and there were question marks over whether he had lost his rugby appetite.
But he took part in two Wales training camps in Poland last month, and looked to have done enough to secure his World Cup place until injury struck again.
Wales, meanwhile, say fly-half Rhys Priestland, who left the pitch at half-time on Saturday nursing a thigh injury, will be re-assessed on Monday.
But both full-back Lee Byrne and wing Leigh Halfpenny have been declared fully fit and in contention for selection against Argentina in the final World Cup warm-up game next Saturday.
Stephen Jones, Ryan Jones and Gethin Jenkins, who all have calf problems, will join Priestland in reporting for injury assessment on Monday morning, when further details about their progress will be established.
Wales say Rees is under "continuous assessment," and they currently have nothing further to report regarding his recovery.
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