A man in his 40s was found dead just after 06:30 GMT at the One-Stop store in Ditton Lane, police said.
Three men, aged 40, 44 and 69 from Cambridge, and a 50-year-old man from Fenstanton have been arrested on suspicion of manslaughter.
A 45-year-old man from Cambridge was arrested on suspicion of grievous bodily harm.
Police said the man who died was from the local area.
A post-mortem examination is due to be held on Tuesday.
Five men have been arrested after a body was found at a convenience store in Cambridge.