The UK tour - set to visit locations including Newcastle, Birmingham and Aberdeen - was announced in July.
However in a statement, Jonathan Church Productions, Curve Theatre, Leicester and Regent's Park Theatre said they were contacted by lawyers acting on behalf of Atticus Limited Liability Company, formed by Scott Rudin, the producer of the Broadway play.
They said the group claimed worldwide exclusivity in the professional stage rights to To Kill A Mockingbird.
The statement added the UK tour had "acted in good faith at all times", but would face legal proceedings if it was not cancelled with immediate effect.
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Organisers are "deeply saddened" at having to cancel the tour, the statement said, and apologised to those who had bought tickets as well as "those currently working to recreate the show which had been in rehearsals until today".
It added: "We are truly sorry for the inconvenience this cancellation will cause and ask that ticket holders contact their original sales point to arrange full refunds."
The Broadway version of To Kill A Mockingbird was adapted for the stage by Aaron Sorkin and opened in New York in December.
It is based on Harper Lee's 1960 novel. US actor Gregory Peck starred as lawyer Atticus Finch in the 1962 film adaption.