Zdenek Makar, 31, from the Czech Republic, died near All Saints DLR station in Poplar on Wednesday night.
The Met said it was believed he had been followed and attacked after an altercation inside Perfect Fried Chicken in East India Dock Road.
Two men, aged 19 and 29, have  also been arrested on suspicion of murder.
A post-mortem examination revealed Mr Makar died from head injuries.
A 16-year-old boy is among three people to be arrested on suspicion of murder following a disagreement at a chicken shop in east London.