Police were called to reports of teenagers armed with machetes during a screening of the new release at the Star City cinema on Saturday evening.
About 100 people were involved in the incident, which left seven officers with minor facial injuries, West Midlands Police said.
Showcase Cinemas has now pulled the film from its listings, following on from Vue, which will no longer be showing the film at any of its 91 UK venues.
Five teenagers were initially arrested following the disorder, including a 13-year-old girl.
Two machetes were seized at the scene and a knife was later recovered from a nearby roundabout.
The disorder is thought to have spilled out into an area of the cinema where parents and children were queuing to watch Frozen 2.
One witness reported seeing a “young boy crying on the floor with his mother” as the fight broke out.
Andrew Onwubolu, who wrote and directed Blue Story, condemned the incident and said his film was about “love not violence”.
Mr Onwubolu, also known as Rapman, described the incident as “truly unfortunate” and said he hoped it was not an “indictment” of the film.
Writing on Instagram, he said: “Sending love to all those involved in yesterday’s violence at Star City in Birmingham.
“It’s truly unfortunate that a small group of people can ruin things for everybody. Blue Story is a film about love not violence.”
The film focuses on two friends from different south London postcodes, on rival sides of a street war.
It is rated 15 for very strong language, strong violence, threat, sex, and drug misuse.
Mr Onwubolu added: “I pray that we can all learn to live with love and treat each other with tolerance and respect.”
A spokesperson for Showcase said: “Due to the recent incidents tied to screenings of the film Blue Story, after careful consideration with the film’s distributor Showcase Cinemas has immediately removed the film from our all of our participating cinemas.
“Any guests that have purchased tickets in advance can receive a full refund at the cinema box office.
“We remain in discussions with the distributor with regards to the possibility of re-introducing the film in due course.
“We apologise for any inconvenience but guest safety remains our top priority.”
Additional reporting by Press Association