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.

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%.