The full extent of the injury was not immediately known but his English Championship (second tier) club coach Aitor Karanka expressed "deep sympathy" for the player who missed the 2010 World Cup finals after damaging his pelvic area.
Williams, expected to be part of Ange Postecoglou's squad for the finals in Brazil, was carried off on a stretcher just before halftime after twisting his body sharply in the league match at the Riverside Stadium.
"They will check him and we will know more soon but it looks like a very serious injury for Rhys," the Spanish head coach told reporters after the game.
"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."
Williams, 25, has played 14 times for Australia after representing Wales at Under-21 level through having mixed parentage.
Australia are in Group B at the World Cup and open their campaign against Chile in Cuiaba on June 13, before matches against Netherlands and defending champions Spain.
(Reporting by Mike Collett; Editing by John O'Brien)
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