In comments carried by the broadcaster, the British Retail Consortium's (BRC) Tom Holder said the move was a temporary measure "to ensure availability for everyone".
Richard Walker, managing director of Iceland supermarkets, said his shops were having to ration sunflower oil sales to one bottle per customer.
"It is not as frenzied as the toilet roll panic buying from a couple of years ago, and we are managing to maintain an offer," he told BBC Radio 4's Today programme.
"But yes, we are limiting purchases and we've moved into smaller packs to allow existing stocks in the market to service more customers."
Most of the UK's sunflower oil comes from Ukraine, with the restrictions applying to that product as well as olive and rapeseed oils at some supermarkets.
Mr Holder from the BRC said retailers were "working with suppliers to ramp up production of alternative cooking oils, to minimise the impact on consumers".
Recent data showed cooking oil was one of a range of food staples to have its price shoot up.
The price of cooking oils and fats went up 7% and is nearly a quarter more expensive than a year ago, the Office for National Statistics said on April 13.
Iceland boss Mr Walker told Today: "If you look at commodity prices, sunflower oil has gone up 1,000% in terms of the commodity cost in the market, palm oil (up) 400% and then there is things like wheat, 50%, fertiliser, 350%.
"These are all unintended consequences of the war in Ukraine that is affecting supermarkets."
A Sainsbury's spokesperson said they have no plans to introduce limits.