Of all the countries in the world to go completely cashless, Sweden could be the first.

It's already considered to be the most cashless society in the world. More Swedes have access to a payment card than to cash, according to data from the country's central bank, the Riksbank. And the overwhelming majority of the nation — 85 percent — have access to online banking.

The Scandinavian country has seen the circulation of notes and coins as a percentage of gross domestic product (GDP) drop year after year, as Swedes make less withdrawals and look to digital methods of paying for things, like cards and mobile.

Just 2 percent of the total value of transactions in Sweden consist of cash, and this is expected to decline to less than half a percent by 2020, according to research by Capgemini and BNP Paribas.

The situation has gotten to a stage where the central bank has had to warn on the rapid rate at which physical cash is being phased out of Swedes' lives.

Earlier this year, Riksbank Governor Stefan Ingves said that a completely cashless society would mean a small number of commercial players being responsible for all payments in Sweden, posing a threat to the infrastructure for payments. A cashless Sweden could be unprepared if faced with a crisis, he added.

Demand for cash would likely increase in a crisis situation, the Riksbank said, but with less notes and coins in circulation, supply would be restrained.

Another problem is that some people in Sweden have little to no access to digital payment services — and some don't want to go digital.

"Our own starting point really is that we provide notes and coins to the society to the extent that society wants to use our version of money versus other versions of money as long as it is safe and efficient," Cecilia Skingsley, deputy governor of Riksbank, told CNBC in a phone interview.

"But we have noticed this rapid development, we have noticed that there are a number of people and there a number of situations and their geographies where cash is absolutely vital."

Elderly people and refugees are among those that would need access to physical cash even if the overwhelming majority of the country don't, Skingsley said.

Sweden could eventually "reach a situation where legal tender is no longer an efficient medium of exchange for commercial transactions and that it is a situation that no other country has been in before," Skingsley said.