NEW DELHI—Early last month, Prime Minister Narendra Modi summoned his cabinet to a room in India’s capital, told them to leave their cellphones outside and delivered a shocker: He was about to go on national television to declare that almost 90% of the country’s paper money would no longer be legal tender.

The move, prepared in secret by Mr. Modi and his advisers, kicked off a radical experiment in government control and instantly put India at the forefront of a nascent global campaign against cash. The European Central Bank has said it would stop printing the €500 note in 2018. Canada and Singapore have phased out their large-denomination bills. The Philippines, Denmark and others are tweaking regulations to nudge citizens to switch to electronic payments.

But no one has gone as far as Mr. Modi. Aiming to cut back tax dodging, terrorism and government corruption, he made India’s largest bank note and one of its most commonly used ones—the functional equivalents of America’s $100 and $20 bills—unusable overnight. Indians can deposit the discontinued bills in a bank before the end of the year to preserve their value. New bills are being rolled out, but so far they amount to only about a quarter of the $230 billion in cash that was voided.

India is hardly alone in seeking to drive underground money into the banking system. But the scale, pace and finality of Mr. Modi’s action make it a stunning and painful test of what had to this point been a largely theoretical debate.

“The great task that the country wants to accomplish today is the realization of our dream of a cashless society,” the prime minister said in a recent radio address.

For a country where few families pay any income tax and even large transactions are often completed in cash, the disruption has been significant—posing new risks for the world’s fastest-growing big economy and Mr. Modi’s popularity.