The accident happened on Thursday at Monte Faito, a peak about 45km south-east of the city, after a supporting cable snapped, Italian media reported.
"What happened is an unimaginable and unpredictable tragedy," said Umberto De Gregorio, chairman of the EAV public transport company which runs the cable car service, on Facebook.
One of the four people killed was a cable car operator from a nearby town, media said. The others were two British and one Israeli tourist, they reported.
A second Israeli was injured and in stable but serious condition, the Naples hospital treating him said on Friday.
Another cabin stopped in mid-air near the foot of the mountain, with 16 passengers evacuated one-by-one with harnesses, footage on RAI TV and other media showed.
Fog and high winds hampered the rescue, Vincenzo De Luca, head of the Campania region around Naples, told RAI.
The cable car services had opened for the spring and summer season 10 days previously, De Gregorio said.
Fourteen people died in Italy in 2021 when a cable car linking the northern Lake Maggiore with a nearby mountain plunged to the ground.
