The exchange took place in a café in the 15th arrondissement of Paris, reported French newspaper Le Parisien.
Trierweiler and a patron of the café got into a heated argument, in which the man used "an ironic tone" when asking the first lady for "news" about her former partner Hollande.
The pair had also been discussing the former first lady's tell-all memoir
about her life with the president, reported RTL radio.
When the man refused to apologize for his remarks, Trierweiler is understood to have slapped him in the face.
The man later reported the matter to police, complaining that he was the victim of assault.
The alleged slap marks the second time Trierweiler has been accused of such an attack.
In September, the former first lady was said to have slapped the face of the ex-wife of Finance Minister Michel Sapin, after allegedly scratching her face and pulling her hair.
Her hot temper, in fact, is becoming somewhat legendary. She was rumoured to have gone on a rampage in the Elysée Palace after learning of Hollande's infidelity with French actress Julie Gayet, smashing €3 million worth of vases, clocks and paintings, all belonging to the Mobilier National.
Those allegations were however rubbished by the Mobilier National, an institution under the culture ministry that is in charge of furnishings in state buildings.
News of the cafe slap was first released by RTL broadcaster, triggering a tweet from Trierweiler saying "A single word #stopboorishness", with no other comment.
A judicial source told AFP the complaint was filed on grounds of violent behaviour.
Under French proceedings that means the plaintiff will have to see a doctor to get a medical certificate stating how long he was unfit to work.
If the inquiry finds the alleged violence did not render him unfit to work for at least eight days, the complaint might lead to a fine by a police tribunal.