Friday’s bombings were concentrated on government buildings and public transportation, with no group claiming responsibility.
A police spokesman said the bombings were clearly co-ordinated by one organisation, but he refused to name what group may have carried out the attacks.
One of the bombs exploded outside a cafe in the capital’s busy Mercato district, killing two people and wounding seven.
Fourteen people had been hurt in three earlier blasts, including two in the northern Piazza commercial district and one on a bus in western Addis Ababa.
Commander Demsash Hailu, a federal police spokesman, said the blasts were the work of an organisation trying to discredit the government.
“We believe the main target of these bombings are the civilians and it is being done intentionally to give an impression that there is no peace or stability in Addis Ababa,” said Demsash.
“We believe all of this is being perpetrated by one organisation,” he added, although he declined to name it.
No group has acknowledged responsibility for the attacks.
The first bombing occurred at an airline office at around 4am (0100 GMT) and shattered windows, although no one was hurt
The other three blasts took place between 9.20 and 9.40am, one damaging the headquarter’s of the city electricity company, injuring seven.
The second bomb went off at the front of a bus, wounding a seven people. The final blast was at the cafe.
Two rebel groups are fighting for regional autonomy from Ethiopia, and small bombs are commonplace in the capital, although they rarely cause significant injuries or damage.
Police have blamed other small bombings in recent months on alleged militant elements of the political opposition.
But with no indication beyond police statements that they were politically motivated, the capital’s residents have been left to speculate that they might be part of a government campaign to smear the opposition.