The other suspects left in a car which was waiting outside the Co-op in Market Street, Ashby-de-la-Zouch, on Thursday night.
During the police arrest, the man, aged 29, fell ill and was taken to hospital.
His death is being treated as unexplained and a post-mortem examination will take place later.
The Independent Police Complaints Commission have begun an investigation into his death.
Police were called just after 22:00 BST on Thursday to reports of a group of men threatening staff with a baseball bat and golf club, and demanding cash.
Officers arrested the suspect, who then fell ill at the scene and was taken to Queen's Medical Centre, in Nottingham, where he died on Saturday morning.
A 24-year-old man who was arrested on suspicion of GBH has been released pending further investigation.
A suspected robber who was stopped by members of the public when a gang threatened and demanded cash from shop workers has died in hospital.