The company, one of the country’s richest and most powerful, said Wu Xiaohui was stepping aside as chairman.
It gave few details but said he was no longer able to fulfil his duties for “personal reasons”.
Chinese business magazine Caijing had reported that Mr Wu was detained by authorities last week, but later deleted its article.
An official source told the BBC that Mr Wu had been taken away from the Anbang Office Building on 8 June by police who arrived in two cars.
It is not clear where Mr Wu is now.
If Mr Wu’s detention is confirmed by the authorities, he would be the highest-profile target of the government’s attempt to re-establish state control of the financial industry, and target corruption.
Anbang is known for a number of high profile international acquisitions, like the purchase of New York’s Waldorf Astoria hotel in 2015.
The company, which manages some 1.65tn yuan (£190bn; $242bn) worth of assets, said in a statement that the chairman’s duties would be managed by other senior executives.
Anbang did not comment on the report by Caijing that he had been detained.
Earlier, Anbang had denied a report by the Financial Times that Mr Wu had been stopped from travelling abroad.