The aircraft came down in thick fog near the Campo Felice ski station after picking up an injured skier.
The rescue was not related to last week's avalanche that engulfed a hotel nearby, killing at least 15 people.
Rescue teams reached the wreckage "and they found the bodies of the six deceased in the snow", a police spokesman told the AFP news agency.
The helicopter was taking the injured skier to hospital in L'Aquila, the capital of Abruzzo province.
Some witnesses reported hearing a loud explosion before it crashed.
Gianluca Marrocchi, mayor of the nearby town of Lucoli, said he saw the helicopter flying very low. "After that it disappeared in the fog," he told RAI state TV.
Campo Felice is a small skiing resort popular with day-trippers from Rome, which is 120km (75 miles) to the west.
It is on the other side of Italy's 3,000m Gran Sasso mountain range from the four-star Hotel Rigopiano, which was engulfed by an avalanche on 18 January triggered by a series of earthquakes. Fourteen people remain unaccounted for there.
Six people have been killed in a rescue helicopter crash in a mountainous area of central Italy, officials say.