The man had been in prison at Gablecross Police Station in Swindon since Saturday morning, but died at 9 a.m. on Sunday.
The Independent Office of Police Conduct is currently investigating the incident (IOPC).
Superintendent Steve Cox said: “The male, who had been kept in custody since Saturday morning, took ill this morning and was regrettably proclaimed dead at before 9 a.m.
“As a result, we made a mandatory reference to the Independent Office of Police Conduct (IOPC), who are currently conducting an independent investigation.
“It would not be appropriate to comment further at this time.”
