The actress has played Roxie Hart for several months on Broadway and was scheduled to begin a four-week run in London from July 11.
Brinkley apologised for the postponement in an official statement, but explained that she needed to help her mother Marge convalesce from an undisclosed medical procedure.
She said: "I am very sorry for the inconvenience and changes to the schedule in London. I thank my producers and new cast mates for being so flexible and understanding and I look forward to giving it my all in dedication to my loving, generous and supportive parents who set me on this 'Broadway adventure', which now leads me to London's prestigious West End, when my Dad said, 'Take it'!"
Sarah Soetaert, who is currently portraying Roxie in the West End production of Chicago, will stay on until Brinkley can join the show.
Brinkley previously revealed that former husband Billy Joel provided her with tips on how to succeed on Broadway.
> Christie Brinkley: "I haven't given up on love"
Watch a clip of Christie Brinkley discuss her role in Chicago during an interview on The View below: