The prosecutor had called for a two-year prison sentence for Khaled Tebboune, whose father did not have any official role at the time of his arrest.
Chikhi, known as "El Bouchi" (The Butcher), made his fortune in meat imports before becoming involved in property.
He was arrested in June 2018 after the seizure of 700 kilograms (1,500 pounds) of cocaine, found hidden in imported meat.
The investigation exposed a network of influence, with accusations that Chikhi, using cash and property, bought favours from high-level officials, magistrates and others within the regime of former president Abdelaziz Bouteflika.
Chikhi was sentenced to 10 years in prison last July on separate bribery charges. A former mayor and the son of a former prefect were also sentenced Wednesday to six and four years in prison respectively.
While prime minister in 2017, Tebboune had launched an attack on oligarchs close to the state who were awarded huge public contracts.
He was sacked just three months after taking office but went on to win the country's presidential election last December. During his presidential campaign, Tebboune said the incarceration of his son sought to "punish" him for his 2017 attack.
Algerians took to the streets over a year ago to demonstrate against ailing Bouteflika's bid for a fifth term.
The alleged links between Chikhi and Khaled Tebboune earned Abdelmadjid Tebboune the nickname "cocaine president" within the protest movement, which marked its one-year anniversary on February 22.