The Web site later added a video it said was shot Tuesday in Brentwood, where the family lives. It shows Shriver holding a cell phone to her ear while driving a large SUV that appears to be a Cadillac Escalade. She then puts the phone down while the camera is rolling.
The first lady's office said it would have no comment.
On his Twitter feed, Schwarzenegger wrote to TMZ.com founder Harvey Levin: "Thanks for bringing her violations to my attention. There's going to be swift action."
Schwarzenegger spokesman Aaron McLear says that by "swift action," the governor means he'll ask his wife not to hold the phone while driving.
In a note accompanying the video, TMZ responded to Schwarzenegger's tweet by saying, "... your scofflaw wife was at it again."
A law that took effect in July 2008 requires California drivers to use a handsfree device when talking on cell phones.
Since then, the California Highway Patrol has issued more than 150,000 citations. That figure does not include citations issued by local police.
Drivers who are spotted by law enforcement officers holding a cell phone to their ear are subject to fines of at least $20 for the first ticket and $50 for subsequent tickets, plus additional fees.
In Los Angeles County, where Brentwood is located, the Superior Court has set the cost at about $93 for the first ticket and $201 for the next one, meaning Shriver would owe at least $300 in fines and court fees had she been caught by police.
Schwarzenegger has previously praised the regulation and said he warned his then-16-year-old daughter that if she ever violated the law, "she'll be taking the bus."
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