Genesis Sicat, 47, of South San Francisco, is suspected of forcibly taking a woman's brown Chihuahua and Pomeranian mix as she was walking on Eucalyptus Avenue at about 11:15 a.m., South San Francisco police Sgt. Joni Lee said.
Sicat had apparently lost a dog that was similar in appearance about a year ago and was convinced the victim's pet was his, Lee said.
He allegedly took the dog off its leash and pushed the woman several times, then ran away with the animal in the 800 block of Second Lane, police said.
Police went to Sicat's home on Saturday and arrested him on suspicion of robbery and battery, Lee said.
The dog was returned to its owner, who had paperwork proving she had adopted the animal from a local shelter.