The epicentre of the quake was recorded at 1059 GMT in the Atlantic Ocean, around 10 kilometres (6.2 miles) west of the island, where many of its 10,000 inhabitants could feel the quake caused by an underwater volcano.
It measured 20 kilometres in depth, the institute said, and was the strongest of the roughly 100 quake that have been recorded on the mountainous island since March 18th.
Earlier Sunday, a smaller, 4.5 magnitude earthquake, was recorded in the same zone, and earlier in the week, two 4.6 magnitude quakes were registered.
On Wednesday, local authorities imposed a number of measures to protect the island's western inhabitants in the light of the increased seismic activities, raising alert levels to the second-highest on a three-scale chart and prompting the closing of some stretches of road.
In October 2011 an underwater volcano erupted off the coast of El Hierro, two days after an earthquake measuring 4.3 on the Richter scale rocked the island.
El Hierro, which means "Iron" in Spanish, suffered thousands of earthquakes throughout much of 2011, prompting officials to briefly close a tunnel linking the island's two main towns — Frontera and Valverde — and evacuate dozens of people over fears of landslides.
The Canary Islands are located off the northwestern coast of Africa. The last major volcanic eruption off the Canary Islands happened off Teneguia, Las Palmas, in 1971.