The earthquake struck at 4.07pm and its epicentre was in the Atlantic Ocean just west of the island, the institute said in a statement. It was measured at a depth of 16 kilometres.
The earthquake was the strongest of the roughly 100 tremblors which were recorded on the island, which has about 10,000 inhabitants, on Wednesday.
The mountainous island has since March 18th been rattled by hundreds of earthquakes caused by an underwater volcano but only a handful have been strong enough for local residents to notice.
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. El Hierro, which has an area of just 267 square kilometres is the westernmost of the seven islands of volcanic origin that make up the archipelago.
The last major volcanic eruption off the Canary Islands happened off Teneguia, La Palma, in 1971.