She and 41-year-old Bardem, who're both from Spain, married in the Bahamas in July. They appeared together in the Woody Allen film "Vicky Christina Barcelona," for which Cruz won the Oscar for best supporting actress in 2009.
In 2008, Bardem won the Oscar for best supporting actor for his role in "No Country for Old Men."
Cruz is headed to London to complete her work on "Pirates of the Caribbean: on Stranger Tides."
The Associated Press contributed to this report.