The Swans will also lose midfielder Justin McInerney to a one-match suspension for a separate high hit on Jack Silvagni in their 16-point win over the Blues.
Amartey, on return from a hamstring injury, collected Boyd high late in the fourth quarter at the SCG on Friday night.
The incident was graded by the match review officer as careless conduct, severe impact and high contact.
Key forward Amartey will be ruled out of Sydney's games against Melbourne, Adelaide and Richmond, after already missing four weeks through injury.
It is a massive blow to an injury-ravaged Swans outfit, with Lewis Melican also serving a three-match suspension for a high hit on GWS tagger Toby Bedford.
McInerney has already sat out for three matches this season for a bump on the Brisbane Lions' Brandon Starcevich.
Sydney lost key defender Aaron Francis to concussion in the second quarter of their Blues win.
Swans coach Dean Cox praised Amartey after the game, but conceded the matter would attract scrutiny from the match review officer.
"I've had a brief look at it, but that will be in the AFL's hands now," Cox said.
"We want to make sure that we play within the rules and this was no different.
"It was good to have (Amartey) back. He provided a really strong focal point for our playing group.
"That's what he does for our footy club and we'll see what action takes from here."
Carlton coach Michael Voss confirmed Boyd will miss at least their clash against the Giants.
"I'm sure they'll get looked at and get looked at very closely and should be treated accordingly," Voss said of the incident.
"'Boydie', he's obviously got concussion protocols now from that hit, so he's not doing so well in there at the moment."
Silvagni did not suffer a concussion after the hit from McInerney, but was substituted out at halftime with groin soreness.
McInerney's bump was graded as careless conduct, medium impact and high contact.
"I haven't seen the Justin one as well as I saw the Joel one," Cox said.
"But our message to the players is get to that line, not over it.
"One thing you want the players to be certainly aware of is there's a line that you need to go to and you can't cross it.
"If you do cross it, there is consequence for that."
Swans defender Joel Hamling was fined $3000 for striking Silvagni in the first quarter.
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