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.

The 24-year-old clocked 101.76 seconds to finish behind Slovakia's Michal Martikan and Sideris Tasiadis of Germany in the third leg of the series.
Martikan took victory by 0.69 seconds on the Markkleeberg course to secure the 20th World Cup gold medal of his career.
"The manner in which I did it today is what I'm happy about," said Burgess.
"Third in the heats, third in the semis, third in the final. That consistency is what I had last year and it's what got me a lot of good results."
The fourth leg of the World Cup is in Ivrea, Italy from 1-3 September.
Women's K1
Ricarda Funk (GER)  103.85 (0)
Jessica Fox (AUS)  106.31 (0)
Eva Tercelj (SLO)  109.17  (0)
Men's C1
Michal Martikan  (SVK)  100.88  (2)
Sideris Tasiadis    (GER) 101.57  (2)
Adam Burgess  (GBR) 101.76  (0)
Five men have been arrested after a body was found at a convenience store in Cambridge.
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Great Britain's Adam Burgess won bronze in the men's C1 at the Canoe Slalom World Cup in Markkleeberg, Germany.