The man was arrested at an address in Luton on Saturday morning on suspicion of domestic violence.
After he was taken into custody, he became unresponsive in his cell and later died reports Sky News.
In a statement, Bedfordshire Police said there was nothing to suggest the death was caused by police action.
The Independent Police Complaints Commission (IPCC) is conducting the inquiry.
Bedfordshire Police Deputy Chief Constable Jon Boutcher said: “The man was taken to custody at Luton Police Station and became ill in his cell, where he was subsequently pronounced dead.
“The IPCC was informed of the incident… No further details will be released in relation to the deceased until a formal inquest has been opened.
“Our thoughts are with the family at this sad time and we will do all we can to co-operate with the investigation and help provide the family, the coroner and the IPCC with accurate information about how and why he tragically died.
“Without prejudice to the ongoing investigation, from what we know at this time there is nothing to suggest this tragic death was caused by any police action, but we are keeping an open mind and we are determined that a full and transparent investigation is conducted so that the causes of this sad loss can be established for the family.