CARACAS, Venezuela—When Henrique Rosales got to the automated-teller machine on Tuesday to withdraw Venezuela’s new currency, he found it dispensed a maximum of 10 sovereign bolivars a day, the equivalent of 15 U.S. cents.

“This money is going to disappear out of my hands in no time,” said the 29-year-old waiter, who said he hasn’t seen cash in five months. He hasn’t been able to pay for bus fare and walks several miles a day from his hilltop slum to the seafood eatery where he works. “I’m realizing the government has no plan...