Ethiopia’s Communications Minister Getachew Reda said the attackers were members of South Sudan’s Murle tribe.
He said security forces were chasing the attackers and had killed 60 so far.
Ethiopia is hosting thousands of South Sudanese refugees who fled the 2013 clashes that began when President Salva Kiir sacked his deputy Riek Machar, accusing him of plotting a coup.
Mr Machar denied the charges, but then mobilised a rebel force to fight the government. He is due to return to the capital Juba to form a transitional government as part of a peace deal.
Mr Reda told the BBC the attackers were not thought to have any links to the South Sudanese government or rebels.
Ethiopia’s Gambella province, where the raid took place, has a history of conflict between communities and a sizable Nuer population, Mr Machar’s ethnic group.
The Murle have previously been accused of carrying out cattle raids and stealing children to raise as their own.