The Justice Ministry says the U.S. filed its request late Thursday and that it has been forwarded to Zurich authorities for an extradition hearing.
It said in a statement Friday that Polanski may appeal the decision if it approves the American request.
The 76-year-old filmmaker was arrested Sept. 26 as he arrived in Zurich to attend a film festival.
Polanski, who won a 2003 directing Oscar in absentia for "The Pianist," was accused of raping the 13-year-old girl after plying her with champagne and a Quaalude pill during a modeling shoot in 1977. He was initially indicted on six felony counts, including rape by use of drugs, child molesting and sodomy.
Polanski pleaded guilty to the lesser charge of unlawful sexual intercourse. In exchange, the judge agreed to drop the remaining charges and sentence him to prison for a 90-day psychiatric evaluation. Polanski was released after 42 days by an evaluator but the judge said he was going to send him back to serve the remainder of the 90 days. Polanski then fled the country on Feb. 1, 1978, the day he was to be sentenced.
A French native who moved to Poland as a child, Polanski has lived in France since fleeing the United States. France does not extradite its citizens.
On Wednesday, Polanski's lawyers split on strategies, with one suggesting for the first time that Polanski might voluntarily return to the U.S. to face justice in California after 31 years as a fugitive.
The new approach emerged after a Swiss court dealt the 76-year-old filmmaker a major setback on Tuesday by rejecting his appeal to be freed from jail because of the high risk he would flee again. Polanski, who has until Oct. 29 to appeal that decision, faces lengthy detention if he is unsuccessful and continues to fight extradition.
"If the proceedings drag on, it's not completely impossible that Roman Polanski might decide to go explain himself in the United States, where there are arguments in his favor," one of his lawyers, Georges Kiejman, told Europe 1 radio.