Video of the unidentified male luring the squirrel to its widely-assumed death went viral earlier this week on YouTube, which has since taken it down.
"It is imperative to find anyone who commits sadistic and violent acts against a vulnerable being," said PETA director Martin Mersereau in announcing the reward.
"Animal abusers are bullies and cowards who look to victimize the most vulnerable, defenseless individuals available to them -- human or nonhuman -- and this man must be caught as soon as possible," he added.
It's not known when the low-quality video was made, but National Parks Service (NPS) spokeswoman Kirby-Lynn Shedlowski said it appears to have been shot along the Grand Canyon's heavily-touristed South Rim section.
"It's an ongoing investigation," she told AFP by telephone, adding that the man and a second, similarly bare-chested male seen in the 15-second video "could be long gone."
One of America's greatest natural wonders, the Grand Canyon National Park gets nearly five million visitors a year. Rules strictly forbid the feeding of its varied wildlife.
In the video, the man -- wearing dark shorts, a straw hat and no shoes -- is seen offering food to the squirrel, with the second man in boxer shorts in the background with a camera.
The man lures the unsuspecting rodent to the edge, then slips a running shoe onto his left foot and gives it a swift kick into the air and into the canyon, which is one mile (1.6 kilometers) deep and up to 18 miles (29 kilometers) wide.
In the United States, harassing wildlife is a federal offense that can result in six months in prison or a fine of up to $5,000.
Britain's Daily Mail newspaper quoted one Jonathan Hildebrand, who supposedly shot the video, as saying he had no part in the incident and did not know the two individuals.
"All I know is that they were French," he was quoted as saying, while PETA said "the perpetrator is rumored to be French or French Canadian."
Shedlowski, who could not recall any similar incident in the past, said: "As far as our investigation is concerned, they are two individuals."