Two brothers surnamed Mak, aged 27 and 28, approached Bay on the set during filming for the American science fiction film and the younger brother demanded payment of HK$100,000 ($12,900), a police spokeswoman told Reuters.
It was not immediately clear why the money was requested.
As a discussion ensued in a busy area of Hong Kong island, the elder Mak walked up and assaulted the director, the spokeswoman said. The elder brother then attacked three police officers who tried to intervene, she added.
The younger brother was arrested on suspicion of blackmail and assault, while the elder Mak was also arrested on suspicion of assault, she said.
Bay sustained injuries to the right side of his face, although he declined to seek treatment, the spokeswoman said, adding she did not believe his injuries were serious.
Filming continued after the dispute.
Bay was not available for comment. When Reuters visited the scene after the assault, the film crew and others working on the set declined to comment.
The three police officers were treated in hospital for minor injuries, while the younger Mak asked to be taken for treatment, saying he did not feel well.
Also arrested at the scene was a third man surnamed Chan.
All three are in custody and police are investigating.
(Reporting By Alexandra Hoegberg and Grace Li; Editing by Anne Marie Roantree and Robert Birsel)
Some are posting that they wanted compensation for the street where their resturant is ,for it being closed down for filiming.Probly not for the films .Tho that would have been a better story.