Power was cut, driving residents from their homes in the port city of Iquique on Monday.
The quake was also felt in the coastal cities of Arica and Antofagasta, in Chile, in the Bolivian capital, La Paz, and in southern Peru.
Acting Chilean Interior Minister Jorge Correa said on Chilean television one man was confirmed dead in a landslide triggered by the earthquake.
Correa said five others died after their car was crushed by a falling boulder on a mountain road near Iquique and two more died of undisclosed causes.
The authorities said that the region suffered power cuts and that telephone communication was down.
"Police, fire and other civil protection agencies are in the area evaluating the situation," Chile's national emergency centre, Oficina Nacional de Emergencia (ONEMI), said in a statement.
"There is no chance of a tsunami," it said, citing an analysis by Chilean naval oceanographers who said the epicentre was in the mountains, not in the ocean.
Local television reported that Iquique, which has a population of about 140,000, and the popular seaside resort of Arica were most affected.
Hotels in Iquique could not be reached by telephone for comment despite repeated attempts.
ONEMI said the epicentre of the quake was 115km northeast of Iquique but was felt throughout northern Chile, a zone of heavy mining activity.
A source at Chile's state-owned Codelco, the world's top copper producer, said the company's operations in the region had not been affected.
"Operations have not been stopped; they remain the same," the source at Codelco's Santiago headquarters said by telephone late on Monday.
Other international mining companies with operations in the region could not be reached for immediate comment.
The US Geological Survey said on its website the quake measured 7.9, meaning it was capable of widespread and heavy damage.
The quake occurred at 6.44pm local time (2244 GMT) and lasted nearly a minute.