The man was arrested at an address in the town at about 08:45 BST on Saturday and taken into custody.
Bedfordshire Police said he later became unresponsive in his cell and died, although they said there was nothing to suggest the death was caused by police action.
The Independent Police Complaints Commission (IPCC) was informed and has started an investigation.
In a statement, Bedfordshire Police said the man had been arrested on suspicion of domestic violence in Purley Centre.
Deputy Chief Constable Jon Boutcher said: "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."
IPCC Associate Commissioner Guido Liguori, who is overseeing the investigation, said: "I would like to offer my sincere condolences to the man's family following his death.
"We are in the process of making contact with them to explain our role."
A 25-year-old man has died in police custody in Luton.