The Swans confirmed on Thursday afternoon that Mills had suffered the setback in last week's hitout against Brisbane, with the malady unlikely to sideline the reigning Bob Skilton Medal winner for long.
First-string ruckman Tom Hickey will miss the opening rounds of the home and away season due to a calf strain, with the AFL journeyman yet to return to running as he looks to complete the conditioning stage of his rehabilitation.
Hickey's setback has opened the door for uncapped ruckman Lachlan McAndrew to potentially make his AFL debut this year, with the mid-season draftee set to compete alongside Peter Ladhams for the starting ruck role for Round 1.
Utility Ryan Clarke (hamstring) and defender Robbie Fox (calf) won't be available for Round 1 due to their respective ailments, while small forward Tom Papley is in a race against the clock to face the Suns after a knock to the ribs at training.
Papley is expected to be available for Round 1, however will need to prove his fitness in the coming weeks.
His new apprentice Jacob Konstanty, who joined the Swans through last year's National Draft as a first-round selection, will spend the coming weeks building his training loads as he looks to overcome shin soreness.
Sydney will name their squad for Friday's pre-season clash with Carlton at 5:00pm on Thursday.