She and Cruise were said to have had a heated argument only a few days ago as he wanted Isabella and Connor to be present at the birth.
Miss Kidman, who is engaged to the country singer Keith Urban, said she believed being in the delivery room could traumatise them.
Suri's arrival in the early hours of Tuesday morning comes after widespread scepticism about her parents' relationship.
Their romance developed incredibly fast - at the exact time both were publicising movies.
There were so many rumours that Miss Holmes was not really pregnant she was forced to pose for pictures showing her bump bared.
Suri's arrival also coincided with a film schedule. Cruise is in the middle of publicising his film, Mission Impossible III.
Yesterday he cancelled a day of promotional work and has not yet decided whether he will fly to London and Rome next week for the premieres in both cities.
He has been a changed man since meeting Miss Holmes last March.
As well as proposing within weeks of their first date, the usually reticent actor jumped on Oprah Winfrey's sofa as she interviewed him and announced: 'I'm in love, I'm in love'.
Photographers and fans have been keeping vigil outside the couple's Los Angeles home for most of the month.
Cruise even had to order a security officer to guard their rubbish bins.
The couple had not revealed the sex of the baby, buying clothes for both girls and boys.
They have taken Scientology-based lessons in parenting.
In preparation for the big day, Cruise bought a new car which would not be recognised by the paparazzi so he could take Miss Holmes to hospital in privacy.
Yesterday the couple were believed to be back at their home where presents had already started arriving from friends including the Beckhams and fellow Scientologists Kirstie Alley and John Travolta.
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