With just eight home-and-away rounds remaining, Amartey is set for at least 10 weeks on the sidelines with a partial tear in his Achilles tendon.
West Coast defender Harry Edwards will also remain on the sidelines for the remainder of the regular season as he looks to continue his AFL career following three concussions this year.
Sydney goalkicker Amartey hurt his Achilles tendon during the club's dour 43-point loss to Brisbane at the Gabba.
The 26-year-old had tried to push through the pain, but managed just three touches, two marks and two behinds before being ruled out in the final quarter.
It is a tough setback for Amartey, who has battled through numerous soft tissue injuries since arriving at the Swans in 2017 to feature in all 15 games this year so far.
Sydney sit second (12-3) ahead of their round-17 fixture against the Western Bulldogs, who are eighth (9-6).
If his recovery tracks exactly to the 10-week mark and Sydney finish in second, Amartey will miss the club's qualifying final following the new wildcard round.
Elsewhere, Eagles defender Edwards will undergo a three-month specialist rehabilitation program in a bid to continue his playing career after fronting the AFL concussion panel.
The 25-year-old has played at AFL level just twice this year after suffering three separate concussions.
He was first concussed in a pre-season match against Port Adelaide, before copping another head knock in the club's round-two win against North Melbourne, and then a round-nine defeat to Melbourne.
Edwards was assessed by the panel of interdisciplinary experts last Thursday.
"Harry has maintained a positive mindset whilst in the concussion protocols," Eagles football boss Gavin Bell said in a club statement.
"And he will undertake the specialist rehabilitation program with the intention of playing AFL next season."
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