Denmark is inching closer to becoming the world's first cashless country after the country's government proposed that retailers should be allowed to only accept mobile and plastic payments. This month, the Danish government unveiled a series of initiatives that included plans to eradicate laws that require stores to accept physical cash.

If parliament gives the go-ahead, clothing retailers, restaurants and gas stations could go cash-free by January 2016.

A worker demonstrates Apple Pay inside a mobile kiosk sponsored by Visa and Wells Fargo. Getty Images

Cards already dominate payment in Denmark, according to a report by payment processing company WorldPay. By 2012, 84.2 percent of Danish transactions were made using cards, with e-wallet payments facing significant growth, the report said. That same year, Ireland was the only other European country that topped Denmark in terms of card payments.

Supporters of the program say less cash at the register will help boost in-store security and cut out resources required for counting and storing coins and bills.

"Cashless environments will make it possible to test new innovative store concepts and payment without having to incorporate the very cost-intensive measures are required when handling cash," Danish Chamber of Commerce CEO Jens Karskov said in a press release.

Read MoreCashless society?Not so fast, new report shows Still, essential services like post offices, hospital cafeterias, dentists and chiropractors will still be legally obligated to accept Danish krone, according to the Danish Finance Ministry's website

Making the change to a completely cashless society will mean overturning tradition, which may be a bigger hurdle than technology, Peter Hahn, a senior lecturer in corporate finance and banking at London's Cass Business School, said.

"This is a cultural issue which requires adoption, and depends on how comfortable people are with plastic," Hahn told CNBC in a phone interview.