The family said they left Bandit, a 10-year-old Maltese, inside their car after they had just arrived from Henderson, Nevada.
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The family went into a restaurant for dinner Wednesday night near Cahuenga and Lankershim boulevards.
When they came out, they discovered someone had broken the rear passenger window, and Bandit, who was inside a canvas dog carrier, was gone.
"We travel with him all the time...I've had him for his whole life, the whole 10 years, and we really need him back," said pet owner Debi.
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Bandit was not wearing a collar, but his owners say he is microchipped.
The thief also took a suitcase from the car.
Anyone who saw the incident or has information is urged to call the Los Angeles Police Department.