Police said that about 10 demonstrators have been arrested so far as scuffles broke out between protesters and police near the Champs-Elysees avenue and the National Assembly.
Paris police confirmed that a demonstrator injured in the hand been treated by paramedics, but did not elaborate.
French Interior Minister Christophe Castaner has gone on Twitter to express his "disgust" as French yellow vest protesters set alight an anti-terror military vehicle at a protest in Paris.
Others threw projectiles at police, who responded with tear gas and stun grenades to disperse crowds.
Paris police said a demonstrator lost four fingers when riot officers stopped protesters from storming the National Assembly.
French Interior Minister Christophe Castaner went to Twitter to express his "disgust" as protesters set alight an anti-terror military auto. The police source, however, said numbers were higher, with 21,000 demonstrators taking part in rallies outside Paris.More news: China has this warning after Modi visits Arunachal Pradesh
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Christophe Castaner, the French interior minister, tweeted a photo of a van belonging to the anti-terrorism police on fire, and said the image filled him with "indignation and disgust".
The Yellow Vest movement is becoming increasingly divided and fractured, with supporters disagreeing on both the means to and the political end game.
The first yellow vest day of protest in November brought 282,000 people out on to the streets across France, according to government figures.
Now, in their 13th consecutive week, the protests have become a sort of an uprising against the French President, Emmanuel Macron, who is seen as out of touch with common people. But France's Interior Ministry said this week's protest was significantly smaller than last week's.
Earlier Saturday, activists in Latvia staged a picket in front of the French embassy in Riga, the capital of the small Baltic EU country, to support the yellow vest movement and urge Latvians to demand higher living standards.