In the second quarter of the Kangaroos' nine-point loss to the Power on Saturday, Curtis ran down Sinn from behind and pinned both arms.
The Port Adelaide defender fell forward and hit his head on the Adelaide Oval turf.
Because Sinn was concussed, the Curtis tackle was graded severe impact, along with high contact and careless conduct.
As it stands, Curtis, who kicked three goals against the Power and has 18 for the season, will miss games against Essendon, Brisbane and Richmond.
The Kangaroos have until Monday morning to decide whether to appeal the suspension.
Losing Curtis, 22, would be a hammer blow given his stellar form.
Kangaroos skipper Jy Simpkin can accept a $1000 fine for instigating a melee with former teammate Jason Horne-Francis, who was slugged $1875 for his second such offence.
Port forward Mitch Georgiades was fined $2000 for tripping Dylan Stephens.
Brisbane's Noah Answerth can accept a $2000 fine for striking St Kilda's Jack Higgins, and Saint Liam Stocker received a $2000 fine for tripping Lion Zac Bailey.
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