The move comes after several alleged incidents of police brutality against pension reform protesters as well as the “yellow vest” anti-government rallies that began more than a year ago.
In the incident filmed during a “yellow vest” protest on Saturday, a man with a bloodied head is seen being held down on his back by a helmeted officer, who then strikes him hard on the face.
The Paris prosecutors' office said it ordered the police oversight body to launch an investigation into “intentional violence by a person in a position of public authority”.
Another video of the incident, filmed near the Gare de l'Est train station by AFP TV, shows the man screaming in pain on his stomach as the officer pins down his elbow with his knee.
“The police chief has asked the department of public order to give a full account of this incident,” the Paris police department said.
The authorities said 60 people were detained during the demonstration, which was again marked by sporadic clashes between protesters and police, with 45 held for questioning afterwards.
The protests were the latest of the weekly Saturday demonstrations held by yellow vests since November 2018, and which have been boosted by opponents of a planned pensions overhaul.
President Emmanuel Macron warned last week that the “unacceptable behaviour” of some officers risked undermining the “credibility and dignity” of the force.
But he also denounced the violence of some extremist protesters who have hurled paving stones and other projectiles at security forces during protests, while smashing storefronts and bus stops or burning vehicles and trash bins.
Prosecutors have also opened an inquiry after a posh brasserie favoured by Macron was targeted in what is being treated as an arson attack before dawn on Saturday.
Firefighters quickly put out the blaze and traces of combustible fuel were later found on the bistrot's heavily damaged terrace — where Macron drew the ire of critics after hosting a lavish party just after winning the first round of the 2017 presidential vote.
“When there are marches and so on, you hear people saying 'Death to the Rotonde, Death to Macron' — it happens all the time: anonymous phone calls, people who enter in the middle of the day saying 'Death to Macron',” Gerard Tafanel, who owns the bistrot with his brother Serge, told AFP.
Unions have called for a new day of demonstrations on Friday, when the government is expected to present a final version of its hotly contested pensions overhaul to Macron's cabinet for approval.
But labour leaders at the Paris transport operator RATP voted on Saturday to suspend a crippling metro and bus strike now in its 46th day, which also led to mass disruptions of national train services.
The strike had already eased recently after the government temporarily dropped a measure that would have required people to work until 64 to have a full pension.
However, an Ifop poll released Sunday showed that 51 percent of respondents backed the strike, while 33 percent were opposed.