YARE, Venezuela— Jean Pierre Planchart, a year old, has the drawn face of an old man and a cry that is little more than a whimper. His ribs show through his skin. He weighs just 11 pounds.

His mother, Maria Planchart, tried to feed him what she could find combing through the trash—scraps of chicken or potato. She finally took him to a hospital in Caracas, where she prays a rice-milk concoction keeps her son alive.

“I watched him sleep and sleep, getting weaker, all the time losing weight,” said Ms. Planchart, 34 years old. “I never thought I’d see Venezuela like this.”

Her country was once Latin America’s richest, producing food for export. Venezuela now can’t grow enough to feed its own people in an economy hobbled by the nationalization of private farms, and price and currency controls.

Maria Planchart has had to go through trash to find food for her one-year-old son, Jean Pierre. She is among a growing number of Venezuelans suffering from hunger and malnutrition. Photo: Miguel Gutiérrez for The Wall Street Journal

Venezuela has the world’s highest inflation—estimated by the International Monetary Fund to reach 720% this year—making it nearly impossible for families to make ends meet. Since 2013, the economy has shrunk 27%, according to local investment bank Torino Capital; imports of food have plunged 70%.

Hordes of people, many with children in tow, rummage through garbage, an uncommon sight a year ago. People in the countryside pick farms clean at night, stealing everything from fruits hanging on trees to pumpkins on the ground, adding to the misery of farmers hurt by shortages of seed and fertilizer. Looters target food stores. Families padlock their refrigerators.

Three in four Venezuelans said they had lost weight last year, an average of 19 pounds, according to the National Poll of Living Conditions, an annual study by social scientists. People here, in a mix of rage and humor, call it the Maduro diet after President Nicolás Maduro.

For more than a month, Venezuelans have protested against the increasingly authoritarian government of Mr. Maduro; by Friday, more than 35 people had been reported killed in the unrest. The country’s Food Ministry, the president’s office, the Communications Ministry and the Foreign Ministry didn’t return calls or emails requesting comment for this article.

“Here, for the government, there are no malnourished children,” said Livia Machado, a physician and child malnutrition expert. “The reality is this is an epidemic, and everyone should be paying attention to this.”

Dr. Machado and her team of doctors are seeing a dramatic increase in emaciated infants brought to the Domingo Luciani Hospital in Caracas, where they work.

The problem is no better in towns like Yare, south of Caracas, where the government’s leftist movement was long popular. “To eat,” said Sergio Jesus Sorjas, 11 years old, “I sometimes go to the butcher and I say, ‘Sir, do you have any bones you can give me?’ ”

The boy receives nutritional formula or a traditional Venezuelan corncake from the parish priest. Sergio said he hasn’t tasted meat in months: “Sometimes, I don’t eat at all.”

The Catholic charity Caritas and a team led by Susana Raffalli —a specialist in food emergencies who has worked in Guatemala, Africa and other regions tormented by hunger—are monitoring conditions here.

The most recent Caritas study of 800 children under the age of 5 in Yare and three other communities showed that in February nearly 11% suffered from severe acute malnutrition, which is potentially fatal, compared with 8.7% in October. Caritas said nearly a fifth of children under age 5 in those four communities suffered from chronic malnutrition, which stunts growth and could mark a generation.

“What’s serious is not that we’re at the crisis threshold, but rather the velocity at how we got there,” Ms. Raffalli said.

By World Health Organization standards, Caritas’s findings constitute a crisis that calls for the government to marshal extraordinary aid. But authorities have resisted offers of food and aid from abroad.

The country’s growing malnutrition is made worse by a breakdown in health care, the spread of mosquito-borne illness and what the Pharmaceutical Federation of Venezuela has called a severe shortage of medicines.

Plenty to want

Belkis Diaz watched her newborn, Dany Nava, wither away last summer from lack of food. There was no baby formula, and Ms. Diaz couldn’t nurse, said Albertina Hernandez, the baby’s grandmother.

“We couldn’t find food, we couldn’t find the milk, and he began to get thinner and thinner,” Ms. Hernandez said.