Albert, ruler of the principality, "officially recognizes a paternity that was legally established a few weeks ago," lawyer Thierry Lacoste was quoted as saying.
Albert had initially planned to keep his parentage of Jazmin Grace Rotolo secret until she reached adulthood, but "the situation had become untenable for her" in recent weeks amid increasing speculation about her father, Lacoste said.
The royal palace refused comment Wednesday on reports about the case, saying it was a private affair of the prince.
French media reports have said Albert had a brief affair with the girl's mother, former waitress Tamara Rotolo, in 1991 when she vacationed on the Cote d'Azur.
The prince's daughter is welcome in Monaco, Lacoste said, but she cannot take the throne and will not bear the Grimaldi family name. Neither will Albert's other illegitimate child, 3-year-old Alexandre.
The 48-year-old ruler, who has never married, unblushingly acknowledged last July that he had fathered the boy out of wedlock with a former Togolese flight attendant, the AP reports.
Last year, Albert told The New York Times that other women had made similar claims. "I don't know of any others that could be true," he said.
Rotolo made a paternity claim shortly after the child was born, he told the Times, but after a U.S. court dismissed the case, he thought the matter had gone away. Since the story of Alexandre hit the media, though, he said she had contacted his lawyer again.