According to police, the two pit bulls attacked the 62-year-old woman in the parking lot of a senior center at 1260 Meadowbrook Road around 11:00 a.m.
As officers arrived on the scene, the dogs turned their attention to them.
As the dogs turned and headed toward the officers, they fired at the dogs, causing both to run behind the Brookside School nearby.
One of the dogs was hit by a bullet, and collapsed and died.
The other dog, described as tan with white on the stomach area, got away.
Authorities are urging residents in the area to remain indoors while they search for the other dog.
The victim identified as Shashi Bala Sharma of Merrick suffered serious injuries, including bruises and cuts to her head and face. She also suffered deep lacerations to heft left arm and both legs.
Sharma remained in critical condition at Nassau University Medical Center treatment for injuries.