A male suspect fired a semi-automatic handgun at the dog-walker, named in US media reports as Ryan Fischer, before making off with the dogs.
The victim was transported to hospital in an unknown condition, Los Angeles Police confirmed to the BBC.
Lady Gaga has offered a reward for the return of her dogs, Koji and Gustav.
A third bulldog, named Miss Asia ran away and was later recovered by police.
Gaga, whose real name is Stefani Germanotta, is currently in Rome working on a new Ridley Scott film, Gucci.