The 32-year-old prop will miss Harlequins’ Gallagher Premiership matches at Northampton on New Year’s Day and at home to Sale on January 8.
Marler was handed a six-week ban, but four weeks have been suspended until the end of the 2023-24 campaign.
The measured RFU disciplinary panel judgement means the in-form front-rower will be available for selection should new England boss Steve Borthwick seek to recall him for the Six Nations.
Marler accepted the charge of conduct prejudicial to the game, having been understood to have insulted Heenan’s mother in Quins’ 15-12 home loss to Bristol on Tuesday.
The Harlequins star apologised to Heenan on social media when prompted to do so by Bristol’s Steven Luatua.
Panel chairman Gareth Graham insisted rugby cannot preach about moral codes and then not put those lofty ideals into practice.
“The player accepted that his conduct was prejudicial to the interests of the game,” said Graham.
"As has been said by previous rugby disciplinary panels, rugby’s core values are not empty words or slogans which can be signed up to and then ignored.
“They are not to be treated as useful bolt-ons dreamt up by a marketing team. They are integral to the game and are what make the game special.
"The insulting and offensive comments made by the player were wholly inappropriate; such comments should form no part of the modern game.”
The suspended four-week ban can be activated at any time until the end of the 2023-24 season should Marler commit a similar offence.
Marler has also been ordered to deliver a presentation to a local club or school and to a Premiership academy, on rugby’s core values.