Brown was running after the ball when it bounced into the path of McCartin in the second quarter of Saturday's derby at the SCG.
The Irishman braced for contact and caught McCartin in the head with his shoulder, dropping the key defender to the ground.
McCartin, 24, had a head injury assessment and was substituted out shortly after, in a game which Sydney won by 29 points.
He has an unfortunate history with head injuries, missing seven games last season with two separate concussions.
His older brother Paddy was forced into retirement through concussions.
Brown's hit on McCartin was assessed by match review officer Michael Christian as careless conduct, high contact and severe impact, drawing a three-match ban.
That ban would rule Brown, 23, out of key matches against Essendon, the Western Bulldogs and Geelong.
He has booted 15 goals in eight games to become a crucial part of the Giants' forward line.
Teammate Toby Greene was offered a $2500 fine for striking Swan Jake Lloyd, while Harry Himmelberg can accept the same fine for tripping James Rowbottom.
North Melbourne veteran Liam Shiels can accept a $2500 fine for striking St Kilda youngster Angus Hastie.
West Coast's Brady Hough was fined $2500 for striking Essendon winger Xavier Duursma.
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