Healy struck Cole's ankle while the Leicester tighthead lay prone once an Ireland maul had collapsed.
The 25-year-old will appear before an independent Six Nations disciplinary committee in London on Wednesday.
His side lost to England 12-6 at the Aviva Stadium in Dublin - the first time this has happened for a decade.
Owen Farrell landed four penalties as England edged a brutal showdown with Ireland to register their first victory in the city since 2003.
Continuous rain took its toll on the match as a spectacle, but it remained a compelling battle of ferocious intensity that was decided by Farrell's kicking accuracy.
lreland will remain in title contention if England lose one of their remaining three games and Declan Kidney refused to concede his team's dream of winning the championship is over.
The recommended suspension for a low-end stamping offence is two weeks, the mid-range five weeks and top-end nine weeks, up to a maximum of one year.
There were scrappy scenes at the match after the stamping incident, although referee Jerome Garces didn't spot the offence at the time.
A two-week ban would see Healy ruled out of Ireland's next Six Nations game against Scotland on 24 February.