One Shepparton Coles supermarket was emptied of any fresh dairy milk on Saturday.
As well as random shortages, the supply issues have led to the introduction of rationing of many dairy products.
Coles said the issue arose because a number of team members at the Laverton chilled distribution centre in Victoria returned a positive test for coronavirus.
Coles has worked with the Victorian Health Department to conduct contact tracing for positive cases, and as a further precautionary measure a significant proportion of team members at the Laverton distribution centre have been asked to self-isolate at home.
Of the team members who have tested positive, none have been present at the Laverton distribution centre since June 25.
“While the Laverton distribution centre has been able to maintain operations, the reduced number of available team members has temporarily impacted our ability to replenish our Victorian stores with chilled and fresh produce lines,” Coles said.
Two-pack purchase limits have now been implemented at all Coles supermarkets, Coles Express and Coles Online in Victoria, as well as at Deniliquin in NSW for products including UHT milk, fresh milk, cheese and butter.