A video compilation posted on social media platform Weibo appears to show workers telling the Chinese visitor they were out of the dessert.
Mini, which is owned by German auto giant BMW, posted an apology over the incident, saying "careless management and staff negligence caused unpleasantness for everyone", and pledged to improve training.
The topic "BMW Mini says sorry" had garnered more than 3.4 million views on Weibo by Thursday afternoon.
Mini representatives told AFP that ice cream stocks had been running low and so hostesses had stopped distributing them to visitors.
The man who was given a tub moments later was a BMW employee, they said, acknowledging the situation was "very unfortunate and might mislead judgement".
China is the world's largest car market and BMW has been at pains to emphasise the importance of Chinese customers at the show.
The Shanghai event is the first time most international industry executives have been back in China since the Covid-19 pandemic.
With domestic brands streets ahead in the crucial electric vehicle sector, BMW has pushed the message that "China is the place to be".
"Munich is where we come from, but China is where we are at home," executive Frank Weber told a news conference Tuesday.
Almost 70 percent of BMW's latest operating system contains functions specific to the Chinese market and the company has tripled its research and development there in the past three years, BMW said.
But the ice cream debacle has sparked online outrage against BMW and reportedly provoked conflicts offline, too.
A video posted to Weibo showed someone placing a bag full of ice creams by a booth at the show shouting: "Free for Chinese people!"
In another incident, a woman livestreamed a confrontation between herself and security guards -- said to have taken place at the Mini booth -- with streaming comments that claimed "BMW is hitting people!"
AFP has contacted Mini for comment.
"BMW executives never expected an ice cream to cause such a big disturbance," one internet user wrote.
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