The incident occurred in the second quarter of the match, with the AFL's Match Review Officer assessing the incident as "careless conduct [with] medium impact [and] high contact".
Franklin's ban comes after AFL great Dermott Brereton admitted that the Swans star would be in trouble at the time of the incident, which saw him catch Ryan in the head with a swinging left arm on the boundary line as he was tackled.
"Lance doesn't have any bigger fan than me, but he's in real trouble for that," Brereton said on Fox Footy's coverage.
"That is considered, it's landed. Just because the boy keeps playing on doesn't mean he didn't elbow him in the face with a considered action. He's in real strife."
Franklin's blow to Ryan's head resulted in a free kick Freemantle's way and caused a momentary scuffle between the two sides on the boundary line.
The suspension puts a dent in Franklin's hopes of reaching the magical 1000-goal mark this season, with just three home and away matches left after this weekend.
Franklin is currently 17 goals short of becoming the sixth player in VFL/AFL history to kick 1000 career goals.
Swans defender Dane Rampe was also cited by the AFL's MRO, charged with tripping Dockers star Michael Walters in the second quarter.
Rampe was hit with a $2000 fine for the trip after it was deemed as "intentional conduct [with] low impact [and] body contact".