The quake, with a preliminary magnitude of 6.4, occurred at 8:15 a.m. about 20 miles off the Ionian Sea island of Lefkada, said the Athens Geodynamic Institute. Its epicenter was about 6 miles under the seabed.
It was followed by at least two strong aftershocks — both with preliminary magnitudes of 5.3, the institute said.
"This reinforces our opinion that the 6.4 was the main quake," said Gerasimos Papadopoulos, a seismologist at the institute.
People raced into the streets and some frightened tourists sought to leave the islands — a potential economic blow during a peak holiday week. The bridge linking Lefkada to the mainland was clogged with cars heading away.
Rescue officials said the main hospital on the island, about 175 miles northwest of Athens, treated at least 21 people for minor injuries. Three others — a Scottish couple and a Czech — suffered serious head injuries in a landslide. The island's fire chief, Alexandros Mihos, said some people suffered broken limbs mostly caused by falling rocks or roof tiles.
Two Italian were tourists injured by fallen rocks at a remote beach, and authorities rescued four rock climbers who were jostled loose and plunged into the sea.
"It was very strong. We were all asleep in my home when it happened and some things, like the television, fell down," said Ilias Georgakis, a resident of Lefkada. "It mostly scared tourists, who have not felt such intense things. We have lived through many earthquakes."
A preliminary survey of Lefkada — the hardest hit area — indicated no serious damage. The most visible problems included cracks in some roads, fallen lamp posts, a collapsed wall in an empty church and a home tilting on its foundation.
Some roads were blocked by landslides and electricity was knocked out in some areas of the island, officials said.
Other Ionian islands reported no major damage. But some older buildings were cracked in Preveza, a mainland port across from Lefkada.
The quake was felt as far away as Athens and parts of southern Italy, officials said.
Seismologists urged bathers to avoid beaches where overhanging rocks could be dislodged by aftershocks. The Civil Defense Agency sent tents for residents too frightened to return home.
The quake hit as residents of the Ionian islands held memorials for the 50-year anniversary of a series of devastating quakes that flattened the island of Cephalonia and killed 476 people.
Seismologists said the 1953 quakes, which included one with a magnitude 7.2, came from a different fault zone.
"We must not connect the two earthquakes," the Geodynamic Institute's Papadopoulos said.
He said the most severe earthquake to hit Lefkada occurred in 1948 with a magnitude of 6.4.
Greece is one of Europe's most earthquake-prone regions and building codes in many of its regions, especially on the Ionian islands, are very strict.
The head of the Lefkada hoteliers union, Theodoros Kondilatos, said none of the island's hotels suffered any damage.
"The hotels of Lefkada, especially those built after 1953 earthquake, were constructed with Japanese earthquake specifications, which are the strictest in the world. The hotels here suffered no damage. The tourists here have nothing to worry about," Kondilatos said.
The deadliest quake in Greece in recent years was a 5.9-magnitude that struck Athens in September 1999, killing 143 people and leaving thousands homeless.