Fighting broke out on Sunday in the Tsorona area, about half-way along the heavily-militarised frontier.
Residents on the Ethiopian side of the border reported hearing gunfire and seeing a large movement of troops and artillery towards the border.
A peace deal in 2000 ended the countries' two-year war but it has not been fully implemented.
The conflict, over the exact location of the border led to the deaths of an estimated 80,000 people.
Ethiopia "unleashed an attack against Eritrea on the Tsorona Central Front. The purpose and ramifications of this attack are not clear," the Eritrean governmentsaid in a short statement issued on Sunday night.
It does not mention any casualties.
Ethiopia's Information Minister Getachew Reda, who is out of the country, told the BBC he was not aware of the fighting.
As part of the Algiers peace agreement signed in 2000 both countries agreed to accept the ruling of an independent boundary commission over the location of the frontier as "final and binding".
But after the commission ruled that the disputed town of Badme was in Eritrea, Ethiopia at first refused to agree to the border demarcation and then called for dialogue before it would implement the decision.
Eritrea rejected this and as a consequence the countries have since been in a state of "neither war nor peace", says the BBC's Emmanuel Igunza in Nairobi.
Clashes at the border have happened in the past but they are rare occurrences.
Eritrea last month marked 25 years since it gained independence from Ethiopia after a long civil war.