Health Minister Amir Aman says on Twitter that the person died at a local hospital in intensive care.
More than 150 people were injured in the blast, several of them critically.
State broadcaster ETV reports that over 30 people have been arrested, including the deputy head of Addis Ababa's police commission.
Witnesses say a man in the crowd tried to throw a grenade at Prime Minister Abiy Ahmed but was restrained by people around him.
Tens of thousands had gathered to cheer a wave of reforms under the young leader, who took office in April.
The ruling party has blamed "desperate anti-peace elements" for the attack.
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