The 33-year-old, named as Steven Chesney, was being held by police in Motherwell on Sunday when he began feeling unwell, and later died.
The Police Investigations & Review Commissioner (Pirc) has now begun an investigation following the death.
A spokesman for the Pirc said: “The Pirc has been directed by the Crown Office and Procurator Fiscal Service (Copfs) to conduct an investigation into the circumstances leading up to the death in custody of Steven Chesney, 33, in Motherwell on May 1 2016.
“A report into the findings of the investigation will be submitted to the Copfs in due course.”
Assistant Chief Constable Malcolm Graham said: “Our thoughts are with the family at this tragic time.
“We can confirm that the COPFS has instructed the Pirc to carry out an independent investigation into the circumstances leading up to the death of a 33-year-old man at Wishaw General Hospital who became unwell on arrival in police custody within Motherwell Police office on Sunday.”