The corporation got the rights more than a decade ago, from Kahlo's niece, Isolda Pinedo Kahlo.
Mattel, however, is saying that they're in the clear, and have been working with the Panama-based Frida Kahlo Corp, whose website claims it has "the support of the Kahlo family" and "is dedicated to educating, sharing, and preserving Frida Kahlo's art, image, and legacy".
Now the late Mexican artist's family alleges the rights to her image have been stolen, and accuses toymaker Mattel of misrepresenting her appearance and ignoring what she stood for.
Over the years the name and likeness of the Mexican artist Frida Kahlo, a fierce feminist and ardent communist, have been associated with a number of unlikely products.
Featuring renowned figures such as Chloe Kim, Patty Jenkins and Frida Kahlo, the company aims to show girls that they can be anything.
While the critics of the doll make legitimate points, there is something to be said for the celebration of Kahlo's life and the impact such a Barbie can have among today's youth.
In a statement, the family insisted Mattel was not authorised to base a doll on Kahlo. "We will talk to [Mattel] about regularizing this situation", said her lawyer, Pablo Sangri, according to The Guardian.
But the latter has violated their contract by failing to inform Kahlo's relatives about the uses of her image, he told AFP. A member of the Mexican painter's family, in fact, disputed Mattel's use of her likeness.
Critics have complained that the doll does not reflect Kahlo's heavy, almost conjoined eyebrows or unibrow, and they say its costume does not accurately portray the elaborate Tehuana-style dresses the artist wore.
Matter vice-president Michelle Chidoni avoided insists that "these dolls are depictions of wonderful women who did incredible things in their time and represent real-life examples and stories for girls to be inspired by", she said.