The victims - a convicted murderer on day release from prison, his partner and her young son - were killed in southern Italy late on Monday after the car they were travelling in was forced off the road by gunmen in a second car, who then fired more than 15 bullets through the windscreen.
Investigators said the child had been riding on the lap of his mother Carla Maria Fornari, who was sitting beside Cosimo Orlando, 43, who had spent 13 years behind bars for the murder of two drug traffickers in the Taranto region before being allowed out on day release.
Orlando is suspected of having used his freedom to try to regain control of the local drug market, and may have been killed by a rival, according to Italian media reports.
Italian Prime Minister Matteo Renzi called the prefect of Taranto to express his "dreadful pain, felt even more as a father than as the prime minister", while the interior ministry sent a reinforcement of 60 policemen to the region to help with the investigation.
The police probe will also look into whether the attack could be linked to Fornari, 30, whose husband was killed in 2011 in another suspected drug war.
Her two other children, aged six and seven, had been travelling in the back of the car and were unharmed.
The governor of the Puglia region, Nichi Vendola, warned of an escalation in violence between organised crime groups for control over lucrative drugs, weapons and prostitution markets.
"The state must react to such a brutal massacre, which clearly shows the inhumane and utterly barbarous code followed by the mafia," he said.
Puglia is home to the Sacra Corona Unita, a mafia-style organization that specialises in fraud, gunrunning and drug trafficking, with links to international crime organizations.
Rosy Bindi, head of the parliamentary anti-mafia commission, said the murders "confirmed that there is no code of honour among mafiosi and never has been. They have always killed women and children."