There have been calls for the UK government to issue urgent protections for the thousands of people in Scotland reliant on the fuel, in places which have long winters and a high proportion of older people.
Police in the Highlands and islands have also warned people that heating oil tanks could be targeted by thieves due to rising demand.
Also speaking on The Sunday Show, Swinney called on the UK government to “stop dithering” and “get on with taking some decision” about reducing energy costs.
He said: “Of course they are dithering, because we’ve had an announcement that something is coming and something is coming and something is coming, and it never comes from the UK government.
“They better get a move on, because people’s heating costs are going through the roof and the UK government is sitting twiddling its thumbs.”
The UK government previously said: “We know that people are concerned about the potential impact of global conflicts on the cost of living.”
“While it is too soon to know the full impact of this crisis, as the chancellor said, she will take the necessary decisions to help families with the cost of living and protect the public finances.”