Graham was named as the 18th man for Brad Fittler's side on Monday morning, but was withdrawn just hours later.
In his place, Penrith Panthers' back Stephen Crichton has been added to the squad after making his Origin debut last year, while Tigers' forward Stefano Utoikamanu was also added as a member of the extended squad.
The Rabbitohs revealed the injury has seen Graham forced to manage his training loads over the early part of each week, something the Blues were unable to work with.
"For a number of weeks, Graham has been managing his training loads at the beginning of each week to allow him to be fit on game day," the club wrote in a statement.
"Unfortunately, this meant he would not be able to be fully involved in the Blues early sessions this week and, as a result, they withdrew him from the squad."
The Rabbitohs didn't stop short of ruling Graham out of this weekend's game against the Canberra Raiders however.
"Graham will return to the Rabbitohs squad today and he will be assessed throughout the week as to whether he is fit to play in Saturday's game against the Canberra Raiders," the club said.