Ethiopia and Eritrea fought a war over their border from 1998-2000 in which more than 80,000 people died. Relations have been tense since and the border remains an issue.
"A bomb exploded on a bus with 25 passengers onboard when it arrived in Sheraro town from Shire town at 9 p.m. (1800 GMT) on Wednesday night," Mustafa Seid, chief of police in Sheraro, told Reuters.
"Thirteen of the passengers are in hospital, six with serious injuries," he said.
Sheraro is about 60 km (38 miles) from Ethiopia's border with Eritrea.
Ethiopia's foreign ministry said in a statement on Sunday that Eritrea had been planning a number of "terrorist" plots to undermine the May 23 national elections.
Ethiopia's parliamentary and regional elections are the first since a disputed 2005 poll ended with street riots in which 193 protesters and seven policemen died.
Top opposition politicians were also jailed after the ruling party said they had provoked the violence to force an unconstitutional change of government.
Mustafa said the bomb was concealed in a bag carried onto the bus by one of the passengers. He said the man was not hurt and was being questioned, but that it was too early to say what the motive for the attack may have been.
An explosion at a cafe in the same region last month killed five people and was blamed by Ethiopian government officials on Eritrea.
The Eritrean government had no comment on that accusation.
