It happened at 6:30 a.m. Monday, after the dog, a boxer, escaped from its yard at 381 Main Street.
Police say when the owner, 56-year old Peggy Place, tried to catch the dog, both were struck by a Ford Explorer heading westbound on Main Street.
Place was transported to Stony Brook University Medical Center where she was listed in critical condition while the dog was taken to an animal hospital.
The driver of the Explorer, Richard Sayler, 51, of Sound Beach, was not injured.