Criticized for lacking efficient vehicles in its lineup, Fiat Chrysler Automobiles NV has taken steps to introduce some of the industry’s most fuel-efficient cars. The problem is few of them are for sale or even being built.

The centerpiece of Fiat Chrysler’s efforts is the new 84-miles-per-gallon hybrid gas-electric Pacifica minivan. But for many potential customers, the vehicle has been as hard to find as the flying pigs, blue moons and two-headed dogs featured in ads for the industry’s first hybrid minivan.

The...