Starring Taron Egerton, the film charts the British singer's rise to fame and his relationship with his former manager John Reid.
Scenes of kissing and sex between men, as well as drug use, contributed to it earning a 15 certificate in the UK.
Principal censor Leiataua Niuapu Faaui told the Samoa Observer that the homosexual activity depicted in the film violated laws and did not sit well in the devoutly Christian country.
However, he did concede that "it's a good story, in that it's about an individual trying to move on in life".
Apollo Cinemas Samoa wrote on Facebook that "due to censoring issues we have had to cancel Rocketman".
About 97% of people in Samoa, which has a population of approximately 200,000 people, identify as Christian.
Gay sex is an offence punishable by up to seven years in prison - even if both parties consent.
Milk, the 2008 film in which Sean Penn portrayed gay activist Harvey Milk, and 2006's The Da Vinci Code - based on the theory that Jesus Christ married Mary Magdalene and bore children - were also banned in the nation.
The Rocketman ban comes the film's gay sex scenes were reportedly cut from the film by a distributor in Russia.
The Moscow Times quoted a Russian critic who first saw the film at its world premiere in Cannes as saying "all scenes with kissing, sex and oral sex between men have been cut", as well as a photo displayed during the end credits featuring Sir Elton and his husband David Furnish.
They said: "We reject in the strongest possible terms the decision to pander to local laws and censor Rocketman for the Russian market, a move we were unaware of until today.
"That the local distributor has edited out certain scenes, denying the audience the opportunity to see the film as it was intended, is a sad reflection of the divided world we still live in and how it can still be so cruelly unaccepting of the love between two people.
"We believe in building bridges and open dialogue, and will continue to push for the breaking down of barriers until all people are heard equally across the world."
Since opening, Rocketman has taken in about $101m (£79.5m) at theatres worldwide.