Cagliari supporters could be heard making monkey noises before and after Kean scored Juventus' second goal of the match. The 19-year-old celebrated by standing in front of the fans with his arms outstretched.
"The best way to respond to racism," Kean wrote on Instagram.
Cagliari captain Luca Ceppitelli appeared to plead with the crowd to stop. He was also hit by a bottle while trying to mediate.
Juventus midfielder Blaise Matuidi, who was abused in the same stadium in January 2018, protested vehemently for the match to be postponed. He appeared to argue with manager Massimiliano Allegri before imploring referee Piero Giacomelli to intervene.
An announcement was then made over the stadium's loudspeakers asking the fans to stop the racist chanting. The message was met with more boos.
However, Juventus defender Leonardo Bonucci, who scored the only other goal in Sardinia, leveled some of the blame at Kean for the way he celebrated his goal.
"Kean knows himself too that he could have done something else," Bonucci said, according to Daniella Matar of The Associated Press. "There were racist boos after Kean's celebration and Matuidi got angry but I think the blame is 50 and 50. Keane made a mistake and the fans made a mistake."
Earlier Tuesday, UEFA president Aleksander Ceferin encouraged referees to halt matches whenever a player is racially abused.
"The moment a match is stopped, or it's not played, I think that 90 percent of normal people in the stadium would kick the asses of those idiots," Ceferin said. "It's 2019, it's not 100 years ago. We will speak to the referees again and tell them to be confident, not to be afraid to act."
Racist incidents have occurred at Cagliari before. While playing for Pescara, midfielder Sulley Muntari was sent off in 2017 for protesting racist abuse. Cagliari weren't punished.