LONDON, Oct 23 (Reuters) - British advertising giant WPP said on Monday it had fired an executive at its GroupM media agency in China after authorities detained the unnamed person on charges of bribery last week.

The executive was one of four people linked to GroupM questioned by authorities in Shanghai, Reuters reported on Saturday, citing two people with knowledge of the matter.

Two former staff were also detained, one of the people said, while the fourth, GroupM China's CEO and country managing director for WPP China, Patrick Xu, was questioned by police but not detained.

WPP, the world's largest advertising group, said it was cooperating with the authorities and it was conducting its own investigation.

"We are terminating the executive's employment with the company, and GroupM is suspending trade with any external organisation we understand to be part of the police enquiries," the company said in a statement on Monday.

"We are absolutely committed to behaving in accordance with the law and our own code of conduct, and will take all necessary action to ensure this is the case within our business."

There has been no official confirmation regarding the nature of the investigation, but one of the sources, who declined to be named citing the sensitivity of the situation, said it was related to rebate mismanagement.

The investigation is likely to reverberate around China's foreign business community, which is already unnerved by a widespread crackdown on consulting and due diligence firms as well as a new national security law.

China is a major growth engine for WPP and GroupM, with global executives vocal about their intention to invest in the market long-term in recent months. (Reporting by Paul Sandle in London and Aatrayee Chatterjee in Bengaluru; Editing by Pooja Desai; editing by David Evans)