According to the IGN, the first one occurred at 2.57 p.m. on Thursday and measured 3.7 on the Richter scale, followed by a 4.6-magnitude quake at 3.44 p.m. local time, which was felt by residents along the coast and in such cities as Pontevedra and Vigo, reports Xinhua news agency.
Then two more lighter tremors measuring 1.9 and 2.5 on the Richter scale took place in the next 13 minutes.
The epicentre of the quakes with a depth of around 3 km was located off the west coast of the region, in the Atlantic Ocean, said the IGN.
Emergency services have reported dozens of calls from local residents, but so far there has been no immediate reports of casualties or severe property damage.
Earthquakes are common in southern and southeastern Spain, but are rarely felt in Galicia.
The worst earthquake recorded in Spain in recent years was a 5.1-magnitude one hitting the city of Lorca in the southeastern region of Murcia in May 2011, killing nine.
