The filmmaker fled the US before sentencing in 1978 after pleading guilty to having sex with an underage girl the year before.
A statement from the Justice Ministry read: "The reason for the decision lies in the fact that it was not possible to exclude with the necessary certainty a fault in the US extraditionary request."
Polanski has already been released from house arrest, Reuters confirms.
The director was arrested last September in Switzerland on the US warrant after visiting the country to receive a lifetime achievement award at the Zurich Film Festival.
He has been kept under house arrest on bail at his alpine chalet since December after being held in custody for two months.