Franklin was booked on the spot by a field umpire for his final quarter sling as the Hawks cruised to a 16.12 (108) to 9.8 (62) victory at AAMI Stadium.
Franklin slung Port utility Paul Stewart to the ground after the Power player lost possession of the ball.
Stewart was stunned by the contact but did not leave the field after an incident similar to that involving Adelaide's Taylor Walker three weeks ago which cost the Crow a two-match suspension.
Franklin booted four goals in the emphatic victory as Hawthorn continued to build ominous momentum with five wins from their past six games.
But his sling tackle took the gloss off the triumph in a match punctuated by heated clashes.
"I don't even know the situation with the report so I'll worry about that on Monday," Hawks coach Alastair Clarkson said.
Hawk Liam Shiels and Port's Danyle Pearce face scrutiny for a prolonged outer wing wrestle in an ill-tempered game, while several other grapples will also be examined.
Hawthorn midfielder Brad Sewell, who was best afield with 33 disposals, said the spiteful nature of the clash was a byproduct of the rivalry between the clubs.
"There was a bit of niggle on both parts from both sides," Sewell said.
"It was based on things that were happening ... a knock off the ball here or there from both sides and that is what happens."
But the Port camp intimated the Hawks were responsible for much of the bitterness.
"That is how Hawthorn play - they were at us," Power coach Matthew Primus said.
The Power's emerging onballer Matthew Broadbent agreed, saying Port refused to be bullied by the Hawks.
"You have got to stand up when any team has a crack at you and that is what we want to do as a team," said Broadbent, among Port's best with 25 touches.
The rolling feuds came despite Hawthorn taking control of the contest early with a dominant opening quarter of 7.4 to Port's 3.3 - and they were never challenged thereafter.
Sewell was the architect and by game's end had logged eight entries into his side's attacking 50 metre arc, with Franklin - who kicked 4.4 - and livewire Luke Breust (three goals) the major beneficiaries.
In contrast, Port had few attacking threats against a stingy Hawthorn defence, with Jay Schulz kicking three goals from limited opportunities.