The two men are believed to be behind a massive garlic smuggling operation whereby huge quantities of the popular seasoning were shipped from China to Norway and then brought over the Swedish border illicitly in order to avoid European Union import duties.
Prosecutors estimate the pair smuggled around €10 million ($13.1 million) worth of garlic into Sweden for distribution throughout the EU.
"We're talking about big money and a profitable operation," prosecutor Thomas Ahlstrand told the local Bohusläningen newspaper.
"It involved many shipments of garlic."
While garlic can be imported to Norway from China duty-free, the EU slaps a 9.6 percent duty on garlic imports.
According to the warrant, the Britons are suspected of using a company set up in Norway to profit from the import duty discrepancy, smuggling more than 100 tonnes of garlic across the Swedish border since 2009.
Prosecutors hope issuing warrants for the pair will result in them being arrested and extradited back to Sweden on charges of aggravated customs violations.