Franklin was caught driving at 90 kph in a 50 speed limit zone in bayside Brighton early on Thursday afternoon.
The injured Hawthorn forward, who was reportedly fined $599 and docked six demerit points for the offence, used Twitter to apologise.
"Hey guys I truly apologise for speeding there are no excuses for it I'm a bloody idiot !!!!" Franklin tweeted.
He has already met with Hawthorn club officials and expressed his remorse.
Franklin, who will miss Saturday's match against Collingwood with a hamstring injury, will face the club's leadership group and management early next week.
Hawthorn coach Alastair Clarkson said it wasn't the right time to deal with the matter.
"We'll deal with it at the appropriate time, but the appropriate time isn't 24 hours before a big game against Collingwood," Clarkson said on Friday.
"There's no matter of urgency in terms of the way we'll treat it.
"There's been an indiscretion.
"'Buddy' has acknowledged that, the club has. We're disappointed it's occurred and he is as well.
"But we'll deal with it on Monday or Tuesday rather than right now."