Addressing the media for the first time since it was revealed he wasn't named an All-Star, Gobert ended his availability abruptly by covering his face and walking away in tears.
Gobert described Thursday as a "rough night" after he was not among the 14 All-Star reserves named.
"My mom called me crying," Gobert said before he shed tears himself. "It was tough. It is what it is."
The 7-footer entered Friday leading the NBA in win shares (8.9) and field goal percentage (.650) while averaging 15.0 points and 12.8 rebounds per game for the Jazz. He also has an NBA-best 6.1 screen assists per game, according to NBA.com tracking data.
Although Gobert, the reigning Defensive Player of the Year, could make the roster as an injury replacement, he said, "It's still not the same as being selected."
Gobert also will miss out on a $1 million bonus for not being selected to the All-Star Game, according to ESPN's Bobby Marks. He would not receive the bonus if selected as a replacement player.
Despite sitting seventh in the Western Conference standings, Utah has zero All-Star selections, which led coach Quin Snyder on Thursday to stick up for Gobert.
"Rudy Gobert should absolutely be an All-Star," Snyder told ESPN. "He's one of the most impactful players in the league. This is clear, not subjective, and shows the process of selecting All-Stars is flawed.
"We talk about defense being valued, but when we have an opportunity to reward it, we reward scoring again and again. Rudy is the best defensive player in the league and an offensive force when you consider his screening, his finishing and the spacing he creates with his presence."
ESPN's Tim MacMahon contributed to this report.