Meng's wife, who has remained in Lyon with their children according to police sources, was receiving protection, it said.
The Hong Kong newspaper said Mr Meng was "taken away" for questioning upon landing in China last week by what it said were "discipline authorities".
Last year, Meng gave a speech on the importance of cracking down on cyber crime which observers said might reflect China's views on the issue.
Meng, 64, the first Chinese head of the worldwide law enforcement agency headquartered in France, was "taken away" for questioning by discipline authorities "as soon as he landed in China" last week, Hong Kong-based South China Morning Post quoted a source as saying.
Roderic Broadhurst, a professor of criminology at Australian National University, said Meng's disappearance would be "pretty disconcerting" for people in global bodies that work with China, and could ultimately damage China's efforts to develop cooperative legal assistance measures with other countries.
When - or if - they reappear, it is often in court.
French police had opened an investigation into Meng's disappearance last week, according to a source close to the inquiry.
Meng's term is scheduled to run until 2020. His wife reported him missing.
That day, she said he sent a message telling her to "wait for my call", before sending the emoji signifying danger.
Also, at one time, China prized Mr Meng's lofty position at Interpol.
"This matter belongs to the global community", she told a press conference. Since then, she lost contact with him.
He used to be Vice Minister of Public Security in China.
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China's recently established National Supervisory Commission holds sweeping powers to investigate the country's public servants with few requirements for transparency.
"It is weird", Broadhurst said Saturday, noting China most likely would "brush off" any political damage to Beijing's involvement in global bodies.
Some critics also view the campaign as a way for Xi to purge the party of political foes.
The Chinese Ministry of Foreign Affairs did not respond to a request for comment from reporters.
"France is puzzled about the situation of Interpol's president and concerned about the threats made to his wife", the ministry said.
It is not clear why Meng - the first Chinese president of Interpol - would be under investigation.
Mr Meng likely dealt extensively with former security chief Zhou Yongkang, who is now serving a life sentence for corruption.
He appointed Meng vice security minister in 2004.
China, in the midst of a weeklong holiday, offered no comment on the disappearance of Meng.
The agency "looks forward to an official response from China's authorities to address concerns over the president's well-being", the statement said.
Interpol has downplayed the concerns, saying the president has little influence over the organisation's day-to-day operations, which are handled by secretary-general Stock, a German.
Under China's supervision law, a suspect's family and the employer must be notified within 24 hours of detention, except in cases where doing so would hinder an investigation.
Interpol co-ordinates searches among its members, issuing yellow notices for missing persons and a red notice - an global alert - for a wanted person.