LONDON—Global oil discoveries fell to a record low in 2016, the International Energy Agency says, raising fresh concerns about the potential for a petroleum-supply shortage as soon as 2020.

The IEA—a Paris group that monitors energy trends for oil-dependent places like the U.S. and Europe—is stepping up its warnings about historically low oil-industry investment during the latest price downturn. Oil companies and producing nations curtailed spending by hundreds of billions of dollars during the price rout, resulting in the...