Phillips sustained the injury at training earlier this week, with the club seeking specialist advice before putting a time frame on his return.
“This time frame still keeps him in contention for round one, but it may be tight so we will see how he goes with the rehabilitation process,” Carlton head of football Andrew McKay told the club’s website.
“We’re looking forward to seeing Andrew back on the park as soon as he can.”
Meanwhile, star midfielder Patrick Cripps is on track to line-up in round one, as he recovers from a stress reaction in his back.
“Patrick Cripps has been travelling really well, he’s back running on the grass now which is fantastic,” McKay said.
“He’s still in line for Round 1 so we’re confident he’ll get to the line and play some good footy from round one onwards.”