Ex-telecom minister Moussa Benhamadi, 67, who was close to ousted president Abdelaziz Bouteflika, contracted the novel coronavirus earlier this month and died on Friday, his brother Abdelmalek Benhamadi told AFP.
He had contracted the disease in prison and been transferred to an Algiers hospital where he died.
Another brother, Hocine Benhamadi, told the website of French-language daily Liberte that the ex-minister had fallen ill on July 4 and was only hospitalised nine days later.
Algeria has declared some 22,000 cases of COVID-19, including more than 1,000 deaths.
Moussa Benhamadi had been held in pre-trial detention at El Harrach Prison since September 2019 as part of an investigation into corruption involving the Algerian high-tech firm Condor Electronics.
Bouteflika, who was Algeria's longest-serving president, was forced to resign in April last year after losing the backing of the army amid massive street protests against his decision to seek a fifth term.
Following his departure, authorities launched a string of graft investigations into members of his entourage accused of abusing their power.
Bouteflika's powerful brother Said and two former intelligence chiefs have been jailed, as have powerful businessmen and former government ministers.
Benhamadi's brother and head of Condor Electronics, Abderahmane Benhamadi, was released in April from provisional detention on suspicion of corruption.
Another brother, Omar Benhamadi, director general of the family business Condor, is still behind bars.