According to news website Btime, the man is believed to have taken the dolphin to his car before driving off with it.
Witnesses said the animal had been found stranded on a beach in Hailing island, and appeared to be dying.
Local officials said the man could face criminal charges if found.
A statement from China's Public Security Department said an investigation into the incident was under way, urging those with information to come forward.
"Dolphins are protected animals in China, so the man will be punished if he is found," the statement on Weibo said.
Footage of the incident, which took place on 1 May, was posted by Btime on Chinese video sharing site Miaopai where it has received more than six million views.