Parker has not played any AFL football for the Swans this season and the suspension means he will not break back into their senior team until well into July, at the earliest.
He was referred directly to the tribunal for the heavy clash last Friday night while playing for the Swans' reserves side.
Sydney pleaded guilty, arguing instead during Tuesday night's lengthy hearing against the severity of his penalty.
Smith was hospitalised after Parker ran past the ball and the incident was graded as careless conduct, severe impact and high contact.
Swans advocate Nick Kidd used GPS data to argue Parker was barely at walking speed when he bumped Smith, to block him from the next contest.
He also used a series of still images from the video footage to contend Smith's injuries were from an accidental clash of heads, immediately after Parker had bumped him.
The medical report said Smith has concussion and facial fractures, plus he will need surgery.
He is expected to be sidelined for six-to-eight weeks.
In his evidence, Parker said he had contacted Smith to apologise and check on his welfare.
"It was no intention of mine to make contact with his head," Parker said.
But VFL advocate Morgan McLay argued Parker had breached his duty of care to Smith in the incident and deserved the six-week ban.
"There's a clear need to protect the head. Everyone's worst fears have occurred," McLay said of the injuries to Smith.
Parker had been unable to return to the Sydney AFL side since recovering from injury a month ago.
He has played 283 senior games for the Swans and they argued in the tribunal hearing Parker deserved a lesser penalty for his good disciplinary record.
"If you look at it really closely, he went to block a player and shepherd a player that was coming through and got it wrong," Swans coach John Longmire said earlier on Tuesday.
"He went to block and he actually wasn't moving, he was stationary at the point of contact. He didn't go high, unfortunately it didn't work out the way that he intended it to do."
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