The team were celebrating winning their seventh straight Serie A title and fourth Italian Cup in a row with an open top bus parade through the streets of Turin.
According to reports, the truck was carrying supporters from one of the team's fan clubs and was closely following the players' bus before becoming entangled in the electric cables of the tram.
Six were injured and two will remain in hospital overnight, one being treated for concussion and the other a neck injury. One fan is reported to be a 38-year-old Italian and the second a 63-year-old Irishman.
Earlier Saturday, club legend Gianluigi Buffon played his final game for Juventus, bringing the curtain down on a 17-year career as the champions enjoyed a 2-1 win over Verona.
It was the first time since 2014 under Antonio Conte that Juventus's players got to celebrate their title with their fans in the streets of Turin where they were greeted by thousands of their supporters.
Coach Massimiliano Allegri this season lead the club to a fourth successive league and Cup double of his reign. But in recent years Juventus skipped the parade because they had qualified for the Champions League final in 2015 and 2017 with the European championships in 2016.
On Saturday, the team left the Allianz Stadium in a fog of smoke from flares and fire crackers after being presented with the Scudetto trophy.
Escorted by scooters, the open top bus made its way towards the city centre along Corso Regina Margherita, one of the longest avenues in the city. Waving flags in the club colours of black and white, with beer and cigars in their hands, the players arrived at Piazza Castello, where the atmosphere hit fever pitch with songs, more fire crackers, green, white and red in the colours of Italy, or the black and white of the jersey of the champions.
The bus then made its way through the throng of supporters along Via Po before finally arriving at Piazza Vittorio Veneto, where it was surrounded by a sea of fans waving flags and scarves in the colours of the club champion of Italy.
In the morning, fans had arrived in Turin from all over Italy for this celebration which also marked Buffon's farewell.
uventus this season won the their 34th Scudetto and 13th Italian Cup.
The number 36 was held aloft on the bus by players as the club also counted the two titles of 2005 and 2006 which the club were stripped of for their role in the calciopoli match-fixing scandal.
By AFP's Emmeline Moore