Giovinazzi began karting in 2000. In 2006, he became the champion in the Italian National Trophy 60cc and Euro Trophy 60 championships. He was champion of the WSK Master Series in the KF2 class in both 2010 and 2011.

Had Giovinazzi won the championship, he would have been the first rookie champion since Nico Hülkenberg in 2009. He would also have been the last ever GP2 champion as the series would become FIA Formula 2 Championship for 2017.

Giovinazzi began his single seater career by competing in Formula Pilota China in 2012. He finished as the overall champion in his debut season with a total of six wins. He also raced for the BVM team in the last round of the 2012 Formula Abarth season at Monza. Despite winning two races and finishing in second place in one, he did not receive any points since he was a guest driver.

After a poor start by finishing outside the points and losing reverse grid pole in the first two rounds, Giovinazzi scored victories in both the feature and sprint races in Baku, becoming the first driver to do ‘the double’ since Davide Valsecchi in 2012.

Giovinazzi competed in the 2013 British Formula Three Championship season with the Double R Racing team, alongside Sean Gelael and Tatiana Calderón. He won two races, at Silverstone and at Spa-Francorchamps, and ended the season as runner-up behind Jordan King. During the season, Giovinazzi entered the 2013 Masters of Formula 3, finishing the race in 10th place.

In 2013, Giovinazzi made his debut in the FIA Formula 3 European Championship with the Double R Racing team. He scored his first points at the fourth round in Brands Hatch, finishing 11th in the first race. His best result of the season was at the final race in Hockenheim, where he finished 6th. Giovinazzi ended the season in 15th place in the championship with 45 points.

In 2014, Giovinazzi signed with Jagonya Agam with Carlin to compete in the 2014 FIA Formula 3 European Championship season. His first Formula 3 podium came with a 2nd-place finish in Hockenheim. His first win came from pole position at the Red Bull Ring, before adding another win at the following round at the Nürburgring. He ended the season in 6th place in the standings with 238 points, recording two wins, seven podium finishes, two pole positions and three fastest laps.

Giovinazzi continued in the championship with Jagonya Agam with Carlin in 2015, in a field which included future Formula One competitors Charles Leclerc, Lance Stroll, George Russell and Alexander Albon. He was a championship contender for much of the season, eventually losing out to Felix Rosenqvist. Giovinazzi ended the season as the championship runner-up, with 412.5 points. He recorded six wins, twenty podium finishes, four pole positions and four fastest laps. During the 2015 season he made his second appearance at the Masters of Formula 3 race, winning the race after starting from 2nd on the grid.

Giovinazzi had impressed Audi Sport Team Phoenix during a DTM test in 2015, before being called up to replace the suspended Timo Scheider for the round at Moscow Raceway during the 2015 DTM season. He finished the races in 19th and 21st.

In 2016, Giovinazzi took part in the Asian Le Mans Series in the LMP2 class alongside Sean Gelael. They entered the final two rounds at Buriram and Sepang, winning both races. Giovinazzi then entered the Silverstone round of the European Le Mans Series alongside Gelael and Mitch Evans for SMP Racing, in which they came 5th.

In the FIA World Endurance Championship, Giovinazzi took part in the 2016 6 Hours of Fuji alongside Gelael and Giedo van der Garde for the Extreme Speed Motorsports team, in which they finished 4th in the LMP2 class. He then took part in the following round in Shanghai alongside Gelael and Tom Blomqvist, finishing 2nd.

On 5 September 2016, it was announced that Giovinazzi would perform simulator work for Scuderia Ferrari. In December, he was confirmed as Ferrari’s third driver.

Giovinazzi remained a reserve and test driver for Sauber and Ferrari in 2018. He took part in six free practice sessions for Sauber during the season.