The singer-songwriter's adaptation of George MacDonald's story was due to open at the Lyttleton Theatre in April, but has had its world premiere postponed indefinitely, The Guardian reports.
The National Theatre has reportedly denied that the project has been cancelled entirely and a spokeswoman told the newspaper: "Development is continuing on The Light Princess and we'll announce a new date for the production in due course."
Amos's long in-production project had already been announced by the National Theatre for its spring 2012 season and would have been helmed by War Horse co-director Marianne Elliot.
It is claimed that the musical has been delayed over fears that it will not be ready in time for the planned premiere. Development workshops had already been held and unannounced castmembers were reportedly told about the delay this week.
Talking to Digital Spy last month, Amos said: "I like involved projects. I'm driven by the idea of characters and the song-cycle form is similar to a musical. I've been working on the musical now it seems like for 5,000 years and that has informed my work.
"I've been studying narrative now for over five years by doing the musical. I don't think I could have done [current album Night of Hunters] had I not been having on-the-chop training with the musical crowd."
> Tori Amos interview: 'It's magical when people embrace your work'
Watch the Tori Amos 'Carry' music video below: