Shares in the group dropped more than 2 per cent in early trading.
The Wall Street Journal, which first reported the investigation, said WPP's board was examining whether Sir Martin had misused company assets, citing unnamed sources.
The group said the investigation is ongoing, and the allegations “do not involve amounts which are material to WPP”.
In a statement, Sir Martin said: "Reports in the media have stated that WPP is investigating an allegation of financial impropriety by me, specifically as to the use of company funds.
"This allegation is being investigated by a law firm. I reject the allegation unreservedly but recognise that the company has to investigate it. I understand that this process will be completed shortly."
He added: "Obviously, I shall play no part in the management of the investigation under way. As a significant share owner, my commitment to the company, which I founded over thirty years ago, remains absolute - to our people, our clients, our shareholders and all of our many stakeholders.
"I do not intend to make any further statement at this time."
Sir Martin was paid £48m last year, a significant reduction on the £70m he pocketed in 2016, after 34 per cent of WPP shareholders voted against his compensation package.
Last month, WPP revealed a fall in like-for-like revenues and billings for 2017, in its worst set of results since the financial crisis.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies