The 25-year-old has been ruled out of action since undergoing surgery earlier this year on a damaged Achilles tendon suffered in January's 0-0 draw with Wigan.
Williams also missed out on the 2010 World Cup through injury and only last month he spoke of his optimism at the possibility of recovering in time for Brazil.
However, Karanka conceded that it would be improbable for Williams to feature in the Championship again during the current campaign and he sympathised with the defender's predicament.
"Rhys is recovering but I don't think it is possible for him to play this season," he told the Gazette.
"It will be a huge blow if he can't go to the World Cup, especially as it happened once before.
"It's the pinnacle of every player's career and to miss out twice is terrible bad luck, I really feel for him."