The video circulated on social media last week showed the young man kicking one of the deer in front of him as he was walking inside the park.
He chased after it and kicked it a second time. He even slapped the head of another deer next to him.
The video has garnered over 16 million views online.
The park is famous for a herd of 1,200 free-roaming sika deer designated a "national treasure" as locals believe they are sacred, according to the Shinto religious tradition.
In the wake of public anger, Japanese authorities called on tourists not to harm deer because it is against the law, Japanese news site Mainichi reported.
Around 50 officials joined a campaign, distributing flyers to tourists with multilingual information on how to properly interact with deer. In addition, local police officers fluent in English and Chinese reminded tourists not to touch the animals.
Any act that harms them can result in prosecution under the Cultural Assets Preservation Law, Asahi news site reported.
Police said they are investigating the tourist’s identity.
In 2021, a man admitted to killing a deer in the park with an ax and was handed a 10-month prison term, suspended for three years.