After teammates of Gobert's on the Utah Jazz, including Donovan Mitchell, also tested positive, the NBA postponed the 2019–20 season until its resumption on July 30 of the same year.

His father, Rudy Bourgarel [fr], is from the French overseas department of Guadeloupe and played college basketball in the United States for the Marist Red Foxes from 1985 to 1988.

[2] Gobert's parents split when he was around three years old; he stayed with his mother in Saint-Quentin and made regular trips to Guadeloupe for his father.

[28] On October 31, 2016, Gobert signed a four-year, $102 million contract extension with the Jazz,[29][30] which at the time made him the best paid French athlete ever (in terms of salary per year).

[33] On January 10, 2017, in a win over the Cleveland Cavaliers, Gobert posted his franchise-best 25th consecutive game with 10-plus rebounds (14).

[38] On March 5, he had 16 points and 24 rebounds and tipped in a missed shot as time expired in overtime to lift the Jazz to a 110–109 win over the Sacramento Kings.

[49] However, after suffering a sprained posterior cruciate ligament (PCL) in his left knee and a bone bruise on December 15, he was ruled out for at least another two weeks.

[55] On December 29, he had a team-high 25 points on 10-of-12 shooting and grabbed 16 rebounds for his 31st double-double of the season in a 129–97 win over the New York Knicks.

[60] On March 25, he scored a season-high 27 points and set the single-season NBA dunk record in a 125–92 win over the Phoenix Suns.

[67] On January 30, 2020, Gobert, alongside teammate Donovan Mitchell, was named a Western Conference reserve for the 2020 NBA All-Star Game.

[68] On March 11, 2020, a game between the Utah Jazz and the Oklahoma City Thunder was postponed right before tip-off after Gobert was placed on the injury list due to illness.

Just two days earlier, after a game against the Pistons in Detroit, Gobert had facetiously touched every microphone and recorder at a press conference concerning the Utah Jazz's response to the virus.

[69] Gobert apologized, saying his actions were careless and exposed others to the disease and that he hopes his story serves as a warning to others to take the virus seriously.

[72] In April, it was reported that his relationship with Mitchell had soured following his careless behavior when infected with COVID-19 and Gobert admitted the two did not speak for some time after.

[73] Gobert has donated $500,000 to help people affected by COVID-19 including part-time employees and COVID-related services.

On June 11, Gobert recorded a playoff career-high 20 rebounds in a Game 2 second-round victory over the Los Angeles Clippers.

[90] On October 20, Gobert made his Timberwolves debut, putting up 23 points and 16 rebounds in a 115–108 win over the Oklahoma City Thunder.

[91] On October 28, Gobert recorded 22 points and 21 rebounds in an 111–102 win over the Los Angeles Lakers; that was his 8th career 20/20 game and first in Minnesota.

[92] On January 6, 2023, Gobert logged 25 points and 21 rebounds on 11-of-15 shooting from the field in a 128–115 win over the Los Angeles Clippers.

[94] On April 9, Gobert was involved in a physical altercation with teammate Kyle Anderson during a game against the New Orleans Pelicans.

[99] On December 2, Gobert scored a personal season-high 26 points on 10-of-12 shooting along with 12 rebounds and 3 blocks in 123–117 win over the Charlotte Hornets.

This was the fourth time he won the award, which ties Dikembe Mutombo and Ben Wallace for the most in NBA history.

Despite his absence, the Timberwolves, led by Anthony Edwards and Karl-Anthony Towns, each scoring 27 points, managed to secure a 2–0 series lead over the defending champions, holding the Nuggets to a 34.9% shooting from the field.

Gobert was called by head coach Vincent Collet to help the senior French national team prepare for the 2012 Summer Olympics tournament.

He was part of the team that won the bronze medal at the 2014 FIBA World Cup, where he averaged 4.1 points per game.

[106] In 2015, he helped France to bronze at the EuroBasket 2015, averaging 10.4 points, 8.1 rebounds, and 2.0 blocks during the tournament,[107] while receiving All-European Championships Second Team distinction's from the website Eurobasket.com.

[109] He also won the bronze medal with France at the 2019 FIBA World Cup, where he averaged 10.1 points, 9.1 rebounds, 1.8 assists, 0.6 steals, and 1.9 blocks per game.

[111] In 2022, he led France to silver at the EuroBasket 2022, averaging 12.8 points, 9.8 rebounds, and 1.2 blocks during the tournament, while being selected to the All-Tournament Team.