Matoub, 42, was killed yesterday near his Berber hometown. He was an outspoken critic of Algeria's violent six-year conflict, attacking both the government and its fundamentlaist Muslim opponents.
He had just returned from exile after surviving a kidnapping by Muslim militants.
Youths took to the streets of several towns in the region of Kabylie, eastern Algeria, and many clashed with police. No arrests were reported.
Thousands of people arrived in the Berber regional capital of Tizi-Ouzou overnight to pay their respects to Matoub, whose funeral will take place on Sunday.
Algeria's security forces said the singer had been "cowardly assassinated" and shot several times.
Matoub was killed outside the village of Oued Aissi, near Tizi-Ouzou.
It was the latest assassination of an Algerian artist during an insurgency that has claimed more than 75,000 lives.
Witnesses said his wife and two sisters-in-law were also wounded in the attack. They said Matoub's car was stopped at a false roadblock, but that the singer drove on. The assailants then showered the car with bullets.