The quakes were centred on the largely rural Afar, Oromia and Amhara regions after months of intense seismic activity.
No casualties have been reported so far.
Ethiopia's government Communication Service said around 80,000 people were living in the affected regions and the most vulnerable were being moved to temporary shelters.
"The earthquakes are increasing in terms of magnitude and recurrences," it said in a statement, adding that experts had been dispatched to assess the damage.
The Ethiopian Disaster Risk Management Commission said 20,573 people had been evacuated to safer areas in Afar and Oromia, from a tally of over 51,000 "vulnerable" people.
Plans were underway to move more than 8,000 people in Oromia "in the coming days", the agency said in a statement.
The latest shallow 4.7 magnitude quake hit just before 12:40 pm (0940 GMT) about 33 kilometres north of Metehara town in Oromia, according to the European-Mediterranean Seismological Centre.
The earthquakes have damaged houses and threatened to trigger a volcanic eruption of the previously dormant Mount Dofan, near Segento in the northeast Afar region.
The crater has stopped releasing plumes of smoke, but nearby residents have left their homes in panic.
Earthquakes are common in Ethiopia due to its location along the Great Rift Valley, one of the world's most seismically active areas.
Experts have said the tremors and eruptions are being caused by the expansion of tectonic plates under the Great Rift Valley.
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