Officers attended Imperial Road in Bedfont just after 6pm on Tuesday (August 16) following reports of an incident involving the man.
A police spokesperson said the men then 'became unwell' and was taken to hospital by ambulance where he died.
The incident has now been referred to the Independent Police Complaints Commission (IPCC) who have launched an independent investigation and the Metropolitan Police Directorate of Professional Standards have been informed.
A spokesperson for the police added that the 29-year-old man's next of kin have been informed of his death.
Another IPCC investigation was launched into Met officers' actions earlier this month after a woman died during a police car chase .