Tesfaye said two people had sustained light injuries but were now on their way out of hospital.
"We haven't apprehended any suspects so far. The case is still being investigated," he added.
Ethiopian officials usually blame such incidents on rebel groups based in the south and south-east of the country.
The attack was the first this year in the Horn of Africa nation, which has faced sporadic explosions during the last four years. Thirteen people were wounded when a bomb ripped through a bus near the border with Eritrea last year, an attack that was blamed on Asmara.
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.