Denmark has become the first country in the world to introduce a fat tax - a surcharge on foods that are high in saturated fat.

Butter, milk, cheese, pizza, meat, oil and processed food will all be taxed if they contain more than 2.3 per cent saturated fat.

Butter, for example, will cost around $1.50 more per kilo.

The tax was designed to limit the population's intake of fatty foods.

Consumers have been hoarding to beat the price rise.

"It has been a chaotic week with a lot of empty shelves. People have been filling their freezers," Christian Jensen of an independent local Copenhagen supermarket said.

"But actually I don't think the tax will make that much difference. If people want to buy a cake, they will buy it."

ABC/AFP