Far-right trolls tweeted threats to gang-rape and kill Del Papa, a leading activist with Jean-Luc Mélenchon's Left Party, after picking up her tweets from the protest against a national meeting of Marine Le Pen's Front National in the southern port city on Saturday.
Some claimed to know where she lives and be able to follow her movements.
When fellow anti-fascists started sending tweets to support her, fake tweets purporting to be threats by her started appearing on the microblogging site.
On Monday police in her home town, Avignon, refused to open a case against her persecutors but the police station has since invited her to return and she is currently compiling a dossier to back up her case.
The Left Party, which claims that a number of its members have been threatened by the far right, has written a letter of protest to Interior Minister Manuel Valls at the initial refusal.
Front National representative, Stéphane Ravier, dismissed the hate campaign as "digital assault", telling regional paper La Provence that party activists had been "insulted and terrorised" by "flesh and blood" individuals.
Paris police arrested 38 anti-fascist protesters after a rally in tribute to murdered Greek activist Pavlos Fryssas on Thursday evening.
A group of far-left demonstrators were heading for a bar frequented by members of the Printemps Français movement, which was born during this year's anti-gay marriage protests, police said, claiming that they were looking for a fight.
About 10 anti-fascists were arrested in Paris last Saturday after clashes with far-right activists.
Police had banned several demonstrations - one in honour of left-winger Clément Méric who was murdered last June and one in support of his killer.