The Australian-born second-rower was stretchered off in the first half of Wales' scratchy 11-10 win over Fiji on Friday night. His hamstring was torn away from the bone in a sickening collision and he may not play again this season.
Wales coach Mike Ruddock confirmed: "The injury needs an operation and Brent is out of action for at least four months, possibly six.
"It's awful news for Brent and his family, as well as the Ospreys and Welsh rugby, who have lost a quality player.
"On the injury front, we are getting a lot more headaches than we would like."
Cockbain, who turns 31 on Tuesday, joins fellow British Lions Gethin Jenkins, Ryan Jones, Dwayne Peel, Tom Shanklin and Gavin Henson on Wales' ever-expanding injury list. As well, three other Wales players - Dafydd Jones, Kevin Morgan and Chris Horsman - limped off during the Fiji match with ankle injuries. Jones and Morgan are unlikely to play against South Africa next Saturday.
As the countdown continues for RWC2015, Tournament Chief Executive Debbie Jevans visited the Millennium Stadium to discuss preparations for the eight matches and reveal the positive news that 100,000 tickets for games at the home of Welsh rugby have sold in the last seven days.
Jason Harries is targeting a first win on the World Series circuit this season with Wales. The series returns to action this weekend in Dubai where Harries is part of a team hoping to build from its efforts in round one in October.
Wales skipper Jevon Groves says his side have addressed a few points from Gold Coast and aim to 'hit the ground running' in the next two rounds of the World Series, kicking off with this weekend in Dubai before heading off to South Africa next week.
Wales Sevens manager Steff Thomas is hopeful his side can build from a quarter-final spot in the opening round of the World Series in Australia when his side take part in the forthcoming double header in Dubai and South Africa.