Dorset Police said officers had restrained the man, who was reported acting erratically in Poole on Tuesday.
The man suffered a medical episode while with the officers, who performed CPR while waiting for an ambulance.
He was taken to Poole Hospital but his condition deteriorated and he died on Wednesday morning, police said. His next of kin have been told.
Police have referred the death to the Independent Police Complaints Commission (IPCC).
A statement from the force said officers were called at 16:12 and 16:19 BST amid concern for the man's welfare.
The statement said: "When officers arrived, a man matching the description was found on The Avenue. He was restrained while officers assessed the situation.
"While with officers he suffered a medical emergency. The ambulance service was requested to attend and officers performed CPR while awaiting their arrival.
"The man was taken to Poole Hospital for further treatment. Sadly, his condition deteriorated and he died in hospital this morning."
A man who police had been called to help after he was seen wandering among traffic has died in hospital.