The reigning Brownlow medallist suffered the injury in last month's State of Origin and, after having surgery, was hopeful of a return in round four against Melbourne on April 5.
He will now consult a specialist this week.
"Our timeline hasn't changed with that," coach Damien Hardwick said on Thursday.
"We will reassess when we get past the bye … then we will make a firmer adjustment about when he's going to make his way back.
"With an injury such as that, it depends on healing."
Rowell's absence hasn't hurt the Suns, who have dominated both Geelong and West Coast in comfortable wins to begin the season.
Champion midfielder Christian Petracca has flourished in his fresh start after a move from Melbourne but Hardwick is still itching to add Rowell to the mix.
"We miss him. You can't replace a Matt Rowell. His toughness around the contest is just something that is irreplaceable," he said.
"There is a reason this guy is one of the best, if not the best player in the AFL.
"He does more than anyone else. A lot of people could learn a lot of things, including our players, off him."
Bailey Humphrey (hamstring) should be fit to face Richmond at the MCG on Saturday after he was a late omission against the Eagles.
Key defender Charlie Ballard is also in the mix after recovering from an anterior cruciate ligament tear to play in the club's last two VFL practice games.
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