The Australian defender - part of the Socceroo squad who will compete at the finals in Brazil - was carried off on a stretcher in pain and taken to hospital after twisting his body sharply just before the break in Boro's goalless draw with Wigan at the Riverside.
"They will check him and we will know more soon but it looks like a very serious injury for Rhys," said the Spanish head coach.
"His face and the doctor's face were not good. He was crying and I feel sympathy for him.
"It is very bad injury for him. I hope he will recover as soon as possible because he had a big chance to play in the World Cup so that will be a big incentive for him.
"All our feelings are with him, mine, the team's, the staff's. He will get all the support we can give him.
"The game was not a good one for us. It was difficult as Wigan are a good team."
Williams missed the World Cup in South Africa in 2010 after suffering a serious pelvic injury.
The game was far from a classic with few chances at either end and Karanka confessed Boro did not deserve to win.
"We did not play with personality and we did not do enough to win the game," he said.
"But when you can not win a game it is important that you do not lose it."
Wigan boss Uwe Rosler, though, was disappointed that his side had had to leave with just a point.
"Before the game I would have taken a point," he said.
"And we started slowly and did not play well in the first half.
"But in the second half we played much better and so I was disappointed because we had the better of the game and had the chances to win.
"In the end we are disappointed to only take one point."