Both chains say it was made to ensure the safety of customers, but some people have been asking why one brawl has affected the whole of the country.
West Midlands Police said the force did not ask for or recommend the film be pulled following Saturday’s violence.
Media playback is unsupported on your device
Media captionBlue Story is the tale of two friends who become rivals
Vue says the decision to withdraw the film “was not one taken lightly or without careful consideration. “
It says the film opened across 60 of its sites on Friday , but during the first 24 hours over “25 significant incidents were reported and escalated to senior management in 16 separate cinemas. “
“This is the biggest number we have ever seen for any film in a such a short time frame.”
It says the film wasn’t pulled based on “biased assumptions”.
What’s the backlash?
Blue Story follows the life of Timmy who lives in Lewisham but goes to school in Peckham – two parts of south-east London that have a notorious gang rivalry.
Its director Rapman said the film is about “love not violence”.
“People are calling the ban discriminatory and institutionally racist,” Sheila Knowles, who’s 24 and runs black events company BBE, tells Radio 1 Newsbeat.
“A lot of people are very agitated because it just seems like a very systematic and targeted attack.”
Some people on Twitter have questioned why Blue Story has been pulled when tha t didn’t happen to The Dark Knight Rises.
William Adoasi, 29, saw the film last week and says it’s “incredible”.
“If anyone’s actually seen Blue Story, they realize that it shows how empty the gangster lifestyle is and and how that street lifestyle is actually robbing people of friendships and relationships. “
He says the decisions made by Vue and Showcase highlighted “negative biases instantly”.
“If a white filmmaker created a film, and it caused an uproar, people would not attribute that to all white people, “he says.
“They wouldn’t shut down every cinema because of one incident. But you’ve got to ask yourself, why have they done that in this instance? And that’s why it’s really upsetting. “
But Errol Lawson, a reformed gangster from Birmingham, said the film was “stirring up” violence.
“The spirit behind it is stirring up this undercurrent, or supporting or fueling this undercurrent, this narrative of violence, youth violence and disregard for life, “he said.
“It’s just showing that you know, we’re not going to value your art as much as we’re going to value mainstream white art, “she says.
” It just really rei nforces the idea that black British art is a threat. “
Image copyright Getty ImagesImage caption Rapman told Newsbeat he hoped people who don’t know much about gang culture would see Blue Story
And both Sheila and William are concerned about how this might impact on young black creatives and
“This may may slow down the production of people’s art and it may even put off investors,” says William.
“If I wanted to now create a film, an investor’s going to think twice about investing into my project, because they ‘ ve seen another young black person’s film get shut down.
“Unfortunately for us, within our demographic, if one person gets shut down, people often view that as a representation of all. “
On the weekend, the hashtags #NoBlueNoVue and #BoycottVue were trending on Twitter.
Vue says the decision to pull Blue Story was not based on “biased assumptions or concern about the content of the film itself “.
In a statement it added:” Blue Story is a fantastic film and one with a very powerful mess age. It is a film that has the opportunity to change lives. We hope that Blue Story achieves the success it deserves and importantly its message does not get lost. “
Newsbeat has contacted Showcase for comment on the allegations.
How often are films pulled?
Image copyright Getty ImagesImage caption The Hunt, featuring Hillary Swank, was due to be released on 27 September
It’s rare for a film to be taken out of the cinema after it’s been classified and released.
In September, a film called The Hunt – a satirical thriller about a group of people in the US who are being hunted by rich people for fun –was pulled from cinemas by its distributorbefore it was released.
One cinema in California reportedly cancelled screenings of the Joker aftera “credible” threatwas made.
Paramount – which is the distributor for Blue Story – says it is “saddened” by the events in Birmingham but said the movie was “important”
“We feel that this is an important film, which we’ve seen play in more than 300 cinemas across the country, with incredibly positive reactions and fantastic reviews. “
What have big UK cinema chains said about Blue Story?
Showcase Cinemas says its decision to pull Blue Story after the Vue incident was made after “careful consideration”.
“The safety of our guests is of the utmost importance , “it says in a statement.
“We remain in discussions with the distributor with regards to the possibility of re-introducing the film in due course.
“We apologize for any inconvenience but guest safety remains our top priority.”
Vue said the decision to remove the film was because “the safety and welfare of our customers and staff is always our first priority”.
Odeon has said while it was not withdrawing the film, it had “a number of security measures in place” for Blue Story screenings.
Image copyright Getty Images 
GIPHY App Key not set. Please check settings