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 period for which government statistics are available—4,074 babies in Venezuela died before reaching a year, up 18.5% from the period last year and more than 50% from that period of 2012.

Infant mortality is rising fast here, at a time when it is falling in almost every other part of the world, in one of the most alarming signals that Venezuela’s social and state structures are unraveling.

“I think it represents a very serious social problem, where the basic functions of governance are breaking down,” said Janet Currie, an economist and expert on infant mortality at Princeton University.

Venezuela’s overall infant mortality rate—defined as deaths within the first year of life—is currently 18.6 per 1,000 live births, according to the most recent government statistics. That is well beyond the upper range of 15.4 Unicef estimates for war-torn Syria.