NEW DELHI—Indian Prime Minister Narendra Modi stunned the country in November when he canceled nearly 90% of its paper money. For weeks, tens of millions of people lined up daily at banks to redeem old bills. Sales at cash-dependent businesses collapsed. The growth of Asia’s third-largest economy slowed to a two-year low.

It was a quintessential move by Mr. Modi, planned in secret with a handful of close advisers. He announced it to the country only hours before it went into effect. His own cabinet ministers knew just 20 minutes...