The ballet was to open Tuesday at the legendary Moscow theatre, with a bevy of international critics in the audience.
But on Saturday the Bolshoi said the premiere had been postponed with no future date set -- a move critics said was unprecedented in the theatre's modern history.
On Monday, the theatre's general director Vladimir Urin announced that the premiere would now be held on May 4, telling a packed news conference that he and artistic director Makhar Vaziev had pulled the show because of poor performances in rehearsals.
"In terms of the quality of the ballet, we realised it was bad," Urin said, adding that the theatre's management was "completely despondent".
But a rehearsal Saturday nonetheless showed a "very serious leap in quality", he said, and the ballet will now have its premiere on May 4.
The ballet has been hotly anticipated given Nureyev's legacy, after his defection to the West and his death from an AIDS-related illness in 1993.
It was created by one of Russia's most innovative theatre and film directors, Kirill Serebrennikov, whose home and Moscow theatre were recently searched in a probe into alleged embezzlement of state funds.
Neither Serebrennikov nor the choreographer Yury Posokhov was present at the news conference, and Vaziev said nothing.
- Gay 'propaganda'? -
Rumours have swirled that Urin was furious at the show's reported nudity and male dancers in drag -- or that he received a call from government officials to pull the show.
Bolshoi ballerina Maria Alexandrova wrote on Instagram: "The last time this happened in the theatre was in the 1930s," during Stalin's Great Terror.
A dancer in the "Nureyev" production, speaking on condition of anonymity, questioned the Bolshoi's public explanation, saying problems during rehearsals are par for the course.
"That's why in the troupe, no one believes the ballet was cancelled for artistic reasons," he told AFP, adding: "No one really believes that it will be staged one day."
Urin insisted there were "no other circumstances" behind the theatre's decision.
But he acknowledged receiving a call from Culture Minister Vladimir Medinsky, known for his conservative views, though he said the minister was simply asking how to comment on the situation to journalists.
Medinsky had a "long conversation with Urin but a ban is not the ministry's style of working," his spokeswoman told the TASS state news agency on Monday.
A source close to the government told the independent TV Rain channel Monday that this week's stagings were cancelled because the ballet was "about freedom for gays" which would "look like a provocation."
Russia has a law banning the "propaganda" of homosexuality to minors, though "Nureyev" has a rating specifying it is for viewers aged 18 and older on posters and tickets.
Urin said "there definitely will be arguments" over the ballet since Nureyev is an "ambiguous figure with a complex fate, and telling this story will be quite difficult."
Referring to the dancer's bisexuality, he said that he realised the ballet addressed a "theme that could prompt a certain non-acceptance from a whole number of people," but insisted that "the artistic content will remain completely unchanged."
The cancelled premiere means "reputational losses undoubtedly, but for us the quality of the ballet is more important," he said.