South Sydney Rabbitohs star Burgess was forced off in the first half of England's 18-4 loss to holders and co-hosts Australia in Melbourne on Friday.
It was feared the 28-year-old would be ruled out for the remainder of the tournament.
But Burgess has now been examined by a knee specialist, prompting England's medical staff to forecast his return to the playing squad "earlier than anticipated".
"It was a blow to lose Sam so early in the game against Australia, but the team coped and competed against the number one side in the competition," England head coach Wayne Bennett said in a statement.
"He'll be a loss, but we expect to see him back soon in the next few weeks and pushing for a place in the squad as we aim to make the quarter and semi-finals.
"Sam's a tough player and he will be doing everything required of him to get fit again. We've got a good team here and everyone is behind each other, on and off the field."
Sam Burgess knee injury update
— England Rugby League (@England_RL) October 28, 2017
Photo Getty Images. Caption: England's Sam Burgess