A district government in the eastern city of Wuxi said in an online statement that investigators concluded that the director of "Hero" and "House of Flying Daggers" and his wife, Chen Ting, flouted family planning policies by having the children without approval and before they got married in 2011.
China limits most urban couples to one child and rural families to two if the first-born is a girl. Zhang, who has a daughter with his first wife, could legally have one child with Chen, but the two were not married when their first child was born and did not have a birth permit, in violation of China's rules.
The fines are based in part on the couple's annual income. The government of Wuxi's Binhu district said they earned a total of about $580,000 in the years before each of the children was born.
Reports that Zhang had violated the country's one-child rule started to circulate in May. Binhu authorities said they were put in charge of the investigation in July because Chen is a registered resident of the district even though she lives in Beijing.
By late last year, Wuxi family planning officials publicly complained they could not get in touch with Zhang, who eventually issued an apology for the "negative social impact" he had created and promised cooperation with investigators.
Zhang's studio confirmed in a statement that Zhang, 63, has fathered two sons and one daughter with Chen, 32, but denied reports of other children Zhang allegedly has fathered with other women.
The case raised questions among members of the public about whether Zhang's social status had allowed him to dodge the family planning rules for years.
The district government said it adopted more severe standards in levying the fines against Zhang and Chen because their violations were particularly flagrant.
Zhang and Chen have 30 days to pay the fines. They may also seek an administrative review or file a court petition if they object to the fines.
Zhang could not immediately be reached Thursday for a response, although he said in December that he would willingly accept any punishment meted out in accordance with state rules.