A man and a woman, both 43, and two girls aged 12 and 8 died in the crash near Quinto, said Ticino cantonal police.
They are believed to be of German nationality and were travelling in a car with German licence plates, reported the Corriere del Ticino.
While the four have not been formally identified, police told newspaper Blick they were a family.
The accident happened when a lorry from Italy driven by an Italian 50-year-old hit the back of the German car, which was at the end of a tailback caused by a traffic jam, according to the papers.
The force of the impact pushed the car into the lorry in front and it was crushed between the two vehicles.
The driver of the Italian lorry was seriously injured and remains in a critical condition in hospital, police said.
Unfall mit mehreren Toten am Gotthard: A2 Richtung Norden bleibt die ganze Nacht gesperrt. https://t.co/gNBISTtPOs- 20 Minuten (@20min) July 26, 2016
Recovering the bodies proved difficult since in order to separate the two lorries, their heavy cargos – water in one, granite in the other – had to be removed first.
The operation was finally concluded in the evening.
The A2 northwards at the southern end of the Gotthard road tunnel was partially blocked causing tailbacks of several kilometres.