The quake on Monday evening in Chile's top mining district also cut off power and burst water mains in and around the port cities of Arica, Iquique and Antofagasta.
Chile's Emergency Bureau ONEMI said most of the quake's victims were killed in landslides. One victim was a 9-month-old baby.
"According to official information we have 11 dead reported," said ONEMI spokesman Mariano Gonzalez.
Television images showed streets littered with giant rocks in Iquique, which has a population of about 140,000, and dozens of collapsed adobe homes in nearby towns.
"Look, the church fell down, 15 houses are destroyed and 20 are uninhabitable. We've been out in the town square all night because it quaked all night. We don't have any food, water or power," Mercedes Cruz, a resident of the town of Huavilla, a town in the mountains near Iquique, told local radio.
The earthquake caused operations to be suspended at only one mid-sized copper mine and briefly affected one other, leaving larger mines unscathed. Chilean mines produce a major portion of the world's copper supply.
The quake hit at 6:44 p.m. (2244 GMT) on Monday and lasted nearly a minute. An earthquake of 7.9 magnitude is capable of causing widespread damage.
Earthquakes of lesser magnitude shook neighboring Peru, as well as Ecuador further to the north, early on Tuesday. They caused minor damage but no injuries, officials in the two countries said.
Chilean government ministers toured the stricken region and President Ricardo Lagos cut short a European tour to travel to the quake area.
Landslides cut off some roads and highways, and emergency crews were clearing the roads.
ONEMI said the epicenter of the quake was 70 miles (115 km) northeast of Iquique. It was felt throughout northern Chile, in the Bolivian capital, La Paz, and in Southern Peru.
- Reuters - Thomson Reuters Foundation
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