The company, which runs a major cannery in Shepparton, set a precedent for corporate Australia by mandating vaccination for workers and contractors earlier this month.
The anonymous online posts suggest defacing SPC products on supermarket shelves and asked what might happen if a needle was found in a can of SPC food, according to reports.
The threats were reported on August 12 and detectives in Shepparton are investigating, police said on Saturday.
Anyone caught contaminating food products faces up to 15 years jail.
SPC has given its workers until the end of November to get vaccinated. As well as not wanting staff to get sick, the company also needs to keep producing essential food.
In mandating the vaccine earlier this month, SPC chairman Hussein Rifai said he wanted to ensure the well-being of workers and the community.
“The Delta variant poses a significant threat to our people, our customers and the communities we serve,” he said in a statement.
All SPC workers will be offered paid time off to get their vaccinations, and two days special paid leave if they become unwell afterwards.
Mr Giles said the company was setting an example for others.
“We firmly believe that it will be manufacturers and innovators like SPC who will help drive Australia’s post-COVID economic recovery,” he said.