The company has sealed and contained all its products after the tests found the virus in the ice cream this week.
"It's likely this has come from a person, and without knowing the details, I think this is probably a one-off," Dr Stephen Griffin, a virologist based at the University of Leeds, told Sky News.
"Of course, any level of contamination is not acceptable and always a cause for concern, but the chances are that this is the result of an issue with the production plant and potentially down to hygiene at the factory."
The expert says the cold temperature, combined with the fat content of the ice cream, could be to blame for the virus' "survival" in the samples. However, Griffin stressed there was no cause for alarm.
"We probably don't need to panic that every bit of ice cream is suddenly going to be contaminated with coronavirus," he added.
The Ministry for Primary Industries said it was not aware of any evidence that New Zealand milk powder was the source of Covid-19.
"In many instances, reports of SARS-CoV-2 detected on food or food packaging are not specific as to how the virus was identified, what amount of virus was found and whether the virus was viable and infectious," the ministry said.
"The scientific literature and experience of global public health authorities is that transmission by airborne droplets and aerosols is the dominant pathway for COVID-19 infection. The risk of transmission by food is considered very negligible."
The company's 1662 employees have reportedly been placed in quarantine.
According to local authorities, the company manufactured 4836 boxes of the ice cream, 2089 of which had been sealed away in storage.
A total of 935 boxes of the ice cream, out of 2747 boxes that entered the market, were in Tianjin. Only 65 were sold to markets.
Authorities have issued a warning for any resident who may have bought the ice cream, asking them to report their health and their movements within the community.