The domestic season will end with the Super League Grand Final on Saturday, 3 October, with England’s first match of the World Cup against Tonga in Perth, Australia scheduled for 17 October.
Williams has been captain of England since 2023.
Brian McDermott, speaking on Thursday after his appointment as England head coach, had said he “did not have any intentions” to change captains prior to the World Cup.
Speaking before kick-off, Warrington head coach Sam Burgess said: “George will probably go for surgery at some point in the next week or two.
“It’s unfortunate for George and the club. There are a number of ways to look at it so we’ve decided to take the positive route. Given the nature of where the injury is, we’re happy that we’ve got hold of it.
“Hopefully he can make a great recovery and we’ll see him back [in action] – if it’s not this year, then hopefully next year.”