There were no immediate reports of casualties or damage.
The first tremor occurred about 37 kilometres north north-west of the city of Concepcion, according to the US Geological Survey.
It was followed an hour and a half later by a 6.0 tremor 25 kilometres north north-west of the same city, which was heavily damaged by an 8.8-magnitude quake nearly a year ago.
The reading was based on the open-ended Moment Magnitude scale now used by US seismologists which measures the area of the fault that ruptured and the total energy released.