Protests in Ziguinchor and the Dakar area erupted on the eve of a scheduled court appearance by Sonko, who is facing trial for the alleged rape of an employee at a beauty salon where he went for a massage.
The trial opened in his absence at a Dakar court on Tuesday and was immediately adjourned until May 23.
Sonko, 48, who was also recently sentenced to a six-month suspended prison sentence for defamation and insults against the tourism minister, has denied the charge.
Sonko, president of the Pastef-Patriots party, came in third in the 2019 presidential elections.
He says the legal cases against him are a plot aimed at barring him from contesting the 2024 vote.
In a statement early Tuesday, the interior ministry said it had been "informed of the discovery of the bodies of two young people."
One of them apparently died of knife wounds in a suburb of the capital Dakar, while the second was found in the southern city of Ziguinchor, it said, without giving further details.
The ministry did not directly attribute the latest deaths to the protests, but said it "strongly urges parents to prevent their children from taking part in violent demonstrations."
These events are liable to "attacks, theft, looting and other acts of vandalism," he said.
On Monday, the ministry said a policeman died after being accidentally crushed by an armored vehicle that had been deployed at demonstrations in Ziguinchor.
Crowds blocked roads with logs and burning tyres, throwing stones at police who responded with tear gas, according to an AFP correspondent there.
Local media reported that several protesters had been injured.
When Sonko was arrested in 2021, several days of protests left at least 12 people dead.