CUMANÁ, Venezuela—Medical staff at the University Hospital in this eastern Venezuelan city delivered two premature infants that needed incubation earlier this year. But because of the shortages plaguing the country, the hospital had only one functioning incubator, forcing staff to make an agonizing choice. They put the stronger of the two babies in the incubator. The other died days later.

Scenes like that continue to play out across this crisis-hit country on a daily basis. In the first five months of this year—the latest...