The official, speaking to Reuters on Wednesday, said nobody had claimed responsibility for the blast.
Addis Ababa put its security forces on heightened alert on Tuesday night after receiving strong evidence that
Somalia's Islamist al Shabaab group was plotting assaults.
It was not clear whether the blast occurred before or after that warning.
"The bomb exploded on Tuesday inside a minibus travelling in Segno Gebeya," government spokesman Shimeles Kemal said, referring to a region bordering Sudan.
"No one has claimed responsibility yet. The case is under investigation."
The warning came three weeks after officials said two Somali suicide bombers accidentally blew themselves up while preparing for an attack on football fans during Ethiopia's World Cup qualifying match against Nigeria.
Al Shabaab has warned Ethiopia of revenge attacks for deploying troops inside Somalia to fight the al Qaeda-linked militants, alongside African Union forces from Uganda, Burundi and Kenya.
The National Intelligence and Security Service also urged the public on Tuesday to inform police if they encountered "suspicious" activity, and urged hotel staff and private landlords to verify the identity of visitors.
Al Shabaab gunmen killed at least 67 people in September when they raided a mall in the neighboring Kenyan capital of Nairobi.
Addis Ababa says it has foiled several attacks in the past few years planned by domestic rebel groups and Somali insurgents.
There have also been sporadic explosions in recent years. Thirteen people were wounded when an explosive device ripped through a bus in the north in 2010, while a bomb explosion near a court in the capital injured two in 2011.