A staff member saw a green truck speeding away from the location when she went to see the puppies, KTLA reported.
Since the Humane Society is not sure if the owner of the dogs is the same person who left them, it has to hold the dogs until Sunday before allowing them to be adopted.
The business does not have security cameras, KNBC reported.
Julio Delacruz, animal services manager at Ramona Humane Society, told KNBC that people usually leave strays and unwanted animals at the society but, normally, they stay to give workers information about the animal's health.
One of the puppies is already accounted for. A black-and-white one will be going home with Chris Loya, who was at the shelter, ready to adopt, when the dogs were found. The dog will be named Oreo, KNBC reported.