"The spreading epidemic is a national security and health issue, which temporarily restricts certain freedoms," Abdelmadjid Tebboune said in a televised speech announcing a ban on all rallies "regardless of their form or nature".
A ministry statement said a 50-year-old man from Blida province south of Algiers, died from the highly contagious virus.
The North African country has so far recorded 60 cases of the COVID-19 illness including a total number of five confirmed deaths, according to official figures.
Algeria has been rocked by more than a year of protests since ageing president Abdelaziz Bouteflika announced a bid for a fifth term in February last year.
He left office under pressure from the street and the army in April but protesters have continued to hold mass rallies demanding sweeping reforms.
Algeria had its first case reported last week, when a 67-year-old man who had heart disease died of the virus, the ministry's director general, Djamel Fourar, told reporters.
The second death was of a 55-year-old Algerian who had returned home from France.
Read also: In under a year Algeria's Hirak did the unthinkable, now it must go one furtherOther patients included two Algerians who had been in France.
Seventeen members of the same family in Blida, southwest of the capital, were infected with the virus, in connection with confirmed cases among Algerians living in France.
The 67-year-old man whose death was announced Thursday was related to the family from Blida, Fourar said.
The health ministry urged Algerians returning from countries with high infection rates to postpone "family visits unless absolutely necessary".
President Abdelmadjid Tebboune, for his part, ordered all Algerian schools to close from Thursday until 5 April, his office said.
Last month, Algerian riot police used water cannons to disperse demonstrators who marked the first anniversary of the mass protest movement that forced the resignation of Bouteflika and continues to seek a complete overhaul of the political system.
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