The quake was also felt in Colombia, where patients in a clinic in the city of Cali were evacuated from the building.
Analysis: Jonathan Amos, BBC science correspondent
Ecuador is used to earthquakes. There have been seven magnitude-7.0 or greater events within 250km of this latest tremor since 1900. And some of these have resulted in very considerable loss of life, not just from the shaking but also from tsunami waves.
The country sits on the so-called "Ring of Fire" - the arc of high seismic activity that extends right around the Pacific basin. At its location, Ecuador fronts the boundary between the Nazca and South American tectonic plates.
These are vast slabs of the Earth's surface that grind past each other at a rate of about 65mm per year. The Nazca plate, which makes up the Pacific Ocean floor in this region, is being pulled down (subducted) and under the South American coast.
It is a process that has helped build the Andes and Ecuador's many volcanoes, including the mighty Chimborazo.
Models that try to forecast the likely casualty numbers from the nature of the quake and local building construction methods indicate this event could be very serious, with the number of deaths running into the hundreds.