Education Minister Najat Vallaud-Belkacem said that the square should be "open to anyone without them being received like this" and Local Authorities Minister Jean-Michel Baylet called on participants to consider where the "magnificent, spontaneous youth movement" was heading.
Labour Minister Myriam El Khomri, whose proposed labour reform is one of the Nuit Debout movement's chief targets, described the incident as "particularly regrettable", while inviting representatives to meet her.
"It's obviously difficult for me to go there at the moment," she told France Inter radio.
Right-wing politicians joined the condemnation, with Eric Ciotti of the mainstream Republicans calling the demonstrators a "far-left minority that presents itself a representing the people while being closed to the French people's true problems".
Marion Maréchal-Le Pen of the far-right National Front called Nuit Debout a "movement that represents nobody and nothing", supported by "young people, school students and students" who "spit on Alain Finkielkraut".
"This democracy is a fairy tale, the pluralism a lie," the philosopher himself declared as he left the square, insisting that he had come to see for himself what was going on but responding bluntly to one woman who was among his tormenters.
Finkielkraut, who was a Maoist in his youth, is called a "neo-reactionary" by his critics, largely because of his vociferous support for Israel, his criticisms of Muslims and his complaints that educational standards are declining.
Varoufakis received a very different welcome earlier on Saturday evening when he compared the movement, which has seen up to 3,000 people sitting in on Place de la République for several weeks, to the occupation of Athens's Syntagma Square in 2011, four years before the left-wing Syriza government, in which he was a minister, was elected.
Violence on the fringes of the protest has also drawn criticism, with more than 400 arrests since it began earlier this month, including 21 on Saturday after a group set fire to wooden palettes and threw objects at the police.
Paris police on Monday congratulated organisers on the fact that there had been no violence or attacks on property for two nights and the square had emptied peacefully early in the morning.
TV broadcast disrupted
Nuit Debout supporters interrupted a popular television broadcast, recorded on Friday and broadcast on Saturday, booing Pierre Gattaz, the head of the bosses' union Medef, while wearing masks of President François Hollande and Economy Minister Emmanuel Macron.
On Twitter they claimed that their identity papers were photocopied after the protest and that some of their number were threatened that they could lose their jobs.