A Finnish tourist has been arrested on suspicion of stealing a piece of volcanic rock from one of Easter Island's iconic statues.

Marko Kulju, 26, faces seven years in prison and a fine of US$19,100 (AU$21,100) if convicted of taking part of the right earlobe from a Moai statue.

The Moai - considered the symbol of Easter Island - were carved from volcanic rock between 400 and 1,000 years ago, and are said to represent the carvers' deceased ancestors.

A local woman told authorities she saw Mr Kulju fleeing from Anakena beach on Sunday with a piece of the four-metre tall statue in his hand.

Earlobe smashed

Police chief Cristian Gonzalez said the Finn was later identified by a number of tattoos the woman saw on his body.

Officers say Mr Kulju used his hands to tear off the earlobe, which fell to the ground and broke into pieces measuring 20 to 30 centimetres each.

"Fortunately, this type of thing does not happen every day," said Easter Island government official Liliana Castro.

"But it does happen, and it is almost impossible to control because on Easter Island there are sites of great archaeological value everywhere and the park guards cannot prevent all such incidents."

National monument

Authorities are inspecting the statue to see if it can be repaired, Mr Castro said.

Damaging Moais is punishable under a law protecting national monuments.

While some of the 400 Moais which dot Easter Island's landscape are more than 20 metres tall, most have an average height of six metres and weigh about 20 tonnes.

The statues gaze out on the south Pacific more than 3,700 kilometres west of Chile, which annexed Easter Island in the 19th century.