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.
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.