Depardieu, 69, is alleged to have met the young Frenchwoman this summer when they worked on an artistic project together, according to French media reports.
Depardieu is thought to be a friend of the woman’s father and had been offering career advice in recent months.
The claims relate to alleged assaiults on August 7 and 13, during informal rehearsals for a play.
A source said the Paris public prosecutor’s office had opened a preliminary inquiry.
The source said: “A complaint was registered on August 27 in the jurisdiction of the Aix-en-Provence prosecutor. The case was passed on to the Paris prosecutor.”
Depardieu’s lawyer Herve Temime last night said the actor has been “shaken” by the allegations, which go against “everything he is and respects”.
He said: “I regret the public nature of this process which poses a major prejudice to Gerard Depardieu, whose innocence I am convinced will be recognised.”
Mr Temime added that Depardieu will “co-operate in the investigation and will answer questions”.
One of France’s biggest film stars, Depardieu has been in more than 170 movies. He rose to international fame when he bagged a Golden Globe for his 1990 role as Georges in the romantic comedy Green Card.
He was also nominated for a best actor Oscar in 1991 for his role in Cyrano de Bergerac. In 2014, he starred in Welcome to New York, a film inspired by the Dominique Strauss-Kahn affair. Former Internation Monetary Fund boss Strauss-Kahn resigned in 2011 following allegations of sexual assault.
Depardieu played a character based on the French politician who is arrested after being accused of raping a hotel maid. The case was settled out of court.
In recent years, Depardieu has hit headlines for his friendship with Russia’s Vladimir Putin and his criticism of the French government.
Putin gave Depardieu a Russian passport in 2013 after he renounced his French citizenship to protest against taxes.
Depardieu branded France a place “populated by foreigners and imbeciles making wine and stinky cheese”.