The Leinster star escaped without a yellow or red card after the controversial incident early in the first half at the Aviva Stadium but citing commissioner Alberto Recaldini of Italy has deemed it worthy of referral.
Television replays appeared to show Healy making contact with Cole's ankle as the Leicester tighthead lay on the floor after the collapse of a maul.
Healy's hearing will be held in London on Wednesday, with the 25-year-old's participation against Scotland, France and Italy now in serious doubt.
The low-end suspension for a stamping offence stands at a fortnight, with a mid-range sanction of five weeks and a top-end punishment of nine weeks to one year.
The former would see Healy sit out the February 24 trip to Murrayfield, while a mid-length suspension would prevent him from playing in the home game against the French on March 9.
While a major ban ruling him out of the entire Lions adventure in Hong Kong and Australia is highly unlikely, a top-end suspension would leave him unavailable until mid-April at the earliest, stopping him from facing Italy on March 16 and leaving him with little time to cement his Lions claims before Warren Gatland names his touring party at the end of that month.