Investigators are looking into the incident after police reportedly insisted Rodrigues's injuries were caused by a crowd-control grenade that exploded near him, a version of events his lawyer "categorically" denied.
Some 2,000 people have been injured in protests since the movement began November 17, notably as weekly demonstrations in Paris routinely descend into clashes between riot police and participants who throw rocks at officers and set fires in the streets.
The bearded Rodrigues, who has become a well-known figure in the "yellow vest" movement with 50,000 followers on Facebook, was live-streaming the protest on the website when he was hit.
Thousands of "yellow vest" demonstrators marched through Paris and other cities on Saturday on the 11th weekend of action against the government, suggesting President Emmanuel Macron has yet to defuse public opposition to some of his policies. Internal police investigators have launched an inquiry, as has the Paris prosecutor.
Referring to rubber projectiles made from French-made weapons, Mr de Veule said: "It was a flash ball".
Some yellow vest leaders want to maintain momentum by holding protests after dark as well as during the day. He accused police of carrying out "all the violence the rules permit".
Mr Castaner said: 'I condemn with the greatest firmness the violence and degradations committed this Saturday again, in Paris and in the provinces, by thugs camouflaged in yellow vests'.
"We don't share all the demands expressed by the yellow vest movement, for instance demands about overthrowing the government [or] brutalising institutions", Laurent Segnis, a member of Macron's centrist Republic on the Move party, said.
On Sunday, will for the first time, a counter-movement to the "yellow West" on the road: A group called "Red scarves" (foulards rouges) called for the early afternoon to March on the Bastille square.
But he is now dubbed the "President of the Rich" with polls showing his popularity rating struggling to get above the 30 per cent mark.