French police announced on Friday that they were leading investigations to find Mr Meng.
The secretary general of Interpol heads the agency, while Meng had the symbolic but powerful position of running its executive committee, which works on official strategy. It did not say why.
Apart from being the Interpol president, Meng also served as a Chinese deputy public security minister.
Concerns over Meng's whereabouts were first raised by wife, who reported him missing to French authorities in the city of Lyon, where the couple live, last Thursday.
On Sunday, after Meng's detention was confirmed, Interpol then announced that he had resigned from his post effective immediately.
Interpol says it has received the resignation of Meng Hongwei, the Chinese president of the worldwide police organisation who went missing one week ago.
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Grace Meng believes her husband to be in danger, AFP reported, citing a statement to reporters in Lyon, France, on Sunday.
Meng was first reported missing after traveling to China September 29.
Speaking in Lyon, the southeast French city where the global police organisation is based, she said the last social media message she received from her husband came on September 25, depicting a single knife emoji. Using his Interpol telephone, he sent her the knife image that day, four minutes after he sent a message saying, "Wait for my call".
Meng's appointment as Interpol president in 2016 alarmed some human rights organisations, fearful it would embolden China to strike out at dissidents and refugees overseas.
Mr Xi has been seeking the return of officials and business people accused of fraud and corruption from overseas, sometimes with the help of Interpol in an arrangement human rights advocates say is prone to abuse.
"This is the last, last message from my husband", she said.
Grace Meng told reporters she thinks the knife was her husband's way of trying to tell her he was in danger.
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Before her husband shared the knife image, she sent him a photo of two animal figurines, one of a bear and another of a horse, meant to represent their two children.
She would not allow reporters to show her face, saying she feared for her own safety and the safety of her children.
The websites of French papers broadcast video clips showing Grace Meng speaking in a trembling voice, with her back to a TV camera in order to hide her appearance.
"This will be deeply embarrassing to China and it may well have to pay a price for its nominee for the presidency of Interpol to be detained for undefined crimes in China, [but] this is of secondary consideration to the party leader if he has a reason to want to take Meng down".
Grace Meng's latest call for help from the worldwide press - an unusual measure for family members of fallen Chinese senior officials - further indicated that Meng and his wife probably had prepared for the worst circumstances.
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