The mother, Irina Belenkaya, was arrested in Hungary while attempting to cross the border to Ukraine with her daughter Elise on Sunday night.
Embassy spokeswoman Irina Zvonova told RIA Novosti that the father, Jean-Michel Andre, was on his way to Budapest, and that when he arrives "Liza will be handed over to him. She is currently at the child protection center in the town of Nyirszolos."
Elise, who has dual Russian-French citizenship, was snatched from her 51-year-old father in southern France on March 20. The Frenchman was severely beaten in the incident, and said that his former wife, Irina Belenkaya, was among the attackers.
Belenkaya could face up to three years in prison.
Zvonova said that under Hungarian law, the authorities must reach a decision by Wednesday evening on whether to detain Belenkaya in custody.
"However, as far as we know the court hearing will be held tomorrow in Budapest," she said. The Russian consul is expected to attend the hearing.
The estranged couple has been embroiled in a "tug-of-war" for custody of their daughter for two years, with Russian and French courts siding with their nationals in the dispute.
Andre was awarded custody by a French court following the couple's divorce in 2007. After his wife left the country, taking her daughter with her, a warrant for her arrest was issued in 2008.
Belenkaya was subsequently awarded custody of Elise by a Russian court the same year.
In response, Andre hired private detectives to trace his wife and child. He then traveled to Moscow to seize his daughter and take her back to France. A Russian court subsequently issued a warrant for Andre's arrest.
