More than 20 people were injured in the blast near Bouira, 120km (75 miles) east of the capital, Algiers.
Al-Qaeda's North Africa wing said it carried out the bomb at the barracks in the village of Lakhdaria.
The attack came as 8,000 athletes from more than 20 sports gathered in the capital for the opening ceremony.
The bomber also died after detonating a refrigerated truck packed with explosives at the military encampment in the mountainous Kabylie region at 0530 local time (0530 GMT).
The owner of a coffee shop in Lakhdaria said: "I heard a terrible explosion.
"I first thought it was an earthquake but soon I found out it was an attack against the barracks."
The All-Africa Games are one of the continent's biggest sporting events.
The BBC's Inas Mazhar in Algiers said there is an unprecedented security presence for the Games.
Some 8,710 police officers and soldiers have been deployed at about 90 locations in the city.
It is the second time that the North African country has hosted the games - the first being in 1978.
Some athletes had expressed concern about going to the games given recent insecurity in the country.
The suicide blast came a day after new French President Nicolas Sarkozy visited Algiers, in his first trip outside Europe since coming to power.
In April, an organisation calling itself al-Qaeda in the Maghreb claimed responsibility for two blasts in Algiers which killed more than 20 people ahead of elections.
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