The French culture minister announced her death on Twitter on Sunday.
French media said Denmark-born Karina had cancer and died on Saturday.
Culture Minister Franck Riester tweeted: "Her look was the look of the New Wave. It will remain so forever.
"Anna Karina radiated, she magnetised the entire world.
"French cinema has lost one of its legends."
Karina made seven films with Godard, her partner at the time, including the 1961 Une Femme Est Une Femme (A Woman is a Woman), in which she played a femme fatale.
For that, she received the best actress award at the Berlin Film Festival.
Other cult Godard movies starring Karina included the 1962 Vivre Sa Vie (Live Your Life) and the 1965 Pierrot le Fou (Pierrot the Madman).
Karina captured film-goers with her large blue doe eyes and acting and singing talents.
The French New Wave broke with traditional cinematic conventions to create a fresh approach to making movies, in keeping with the free-spirited times.
Godard was not the only director with whom Karina worked.
Jacques Rivette's 1966 film La Religieuse (The Nun), adapted from the 18th-century French novel by Diderot, was initially banned.
The story of a young woman forced into the convent by her mother, who had given birth out of wedlock, was revived in a restored version and presented at the 2018 Cannes film festival.
Born Hanne Karin Blarke Bayer in Denmark, she initially modelled and sang in cabarets before moving to France.
She was reportedly renamed by Coco Chanel then discovered by Godard.
Karina also worked, among other illustrious directors, with Luchino Visconti.
In a bold undertaking at the time, the actress later got behind the camera to make her own movie in 1973, Vivre Ensemble (Living Together).