The outbreak of Highly Pathogenic Avian Influenza (HPAI), a bird flu which spreads rapidly in an infected flock causing a high death rate, has already impacted table egg supplies in the country and producers have warned of chicken meat shortages in the coming weeks.
Rainbow is one of South Africa's largest chicken producers, supplying retailers and fast food businesses.
"The outbreak has moved at a rapid pace, and the situation is constantly evolving. To date an estimated 410,000 birds have been culled, which has resulted in an estimated financial impact of R115m ($5.99m)," RCL Foods said in an update.
The company said it was taking steps to avert supply disruptions, but "there is tension in the supply chain".
On Wednesday, neighbouring Namibia suspended poultry imports from South Africa, citing the bird flu outbreak. However, South Africa only exports between 1% and 2% of its production, according to the country's poultry producers' association.
Last week, RCL's peers, including the country's largest integrated poultry processor Astral Foods and Quantum Foods, said the bird flu outbreak was ravaging a sector that was already burdened by South Africa's electricity crisis and rising costs.