The Simi Valley-based Southern California Pit Bull Rescue announced the reward, saying its founder was offering the money in an effort to identify whoever shot the coyote.
"Someone shot her. Someone may know who did it," the organization said in a social media post. "Someone may have heard a person talk about shooting a coyote in the Studio City area. Maybe they saw something. Maybe they know something they didn't think was important at the time."
The group urged anyone who may have seen something or heard someone discuss shooting a coyote in the Studio City area to come forward.
Wendy, believed to be about 3 years old, had lived with a large growth or abscess on her face for more than a year and had become familiar to residents in Studio City.
Wildlife Care of Southern California captured her last week after tracking sightings reported by residents since July.
Following her capture, Wendy was given antibiotics and anti- inflammatory medication and fed soft foods she was able to eat despite her condition, officials said.
A veterinary examination and diagnostic imaging later revealed two pellets lodged in Wendy's head and a severe infection that had destroyed the upper jaw bone on the left side of her face, according to Wildlife Care of Southern California.
"The extent of the damage was so severe that there was no surgery or treatment capable of restoring normal function," the wildlife organization said Tuesday.
Veterinarians determined Wendy would have required a soft-food diet for the rest of her life and could not have been returned to the wild.
"After consulting together and carefully considering her long-term welfare and quality of life, we collectively determined that keeping her alive under those circumstances would not be humane," Wildlife Care of Southern California said.