The pair have been married since June and Urban announced last week that he was seeking treatment for alcohol abuse.
According to Fox News, she has also cancelled her appearance at the high-profile New York City premiere on Sunday night, leaving costar Robert Downey Jr. and director Steven Shainberg to promote the film.
Kidman stars in the film as famed American photographer Diane Arbus, who was noted for her portraits of people on the fringes of society.
The Moulin Rouge star has returned to London where she is filming His Dark Materials: The Golden Compass, while Urban remains in rehab in Nashville.
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