The league's disciplinary panel acknowledged in a statement that there were chants, which it described as "certainly reprehensible" but said they had "limited" relevance and perception.
"No sanction will be applied to Cagliari," it said.
The match took place on April 2 but the tribunal had postponed a decision to obtain more information from match delegates.
Kean, who had been jeered throughout the game, stood in front of the Cagliari fans behind the goal and opened his arms after scoring Juve's second in their 2-0 win near the end of the match.
In response, Cagliari’s supporters made the noise which is described by Italian media as “buu” and is regarded as a racist insult in Italian football, although some fans argue it is simply to annoy opposing players regardless of race.
Monkey noises could also be heard among the crowd.
Shortly after the goal, Juve’s French midfielder Matuidi protested furiously to the referee.
Italian football has been plagued by racism and authorities have been criticised for not taking strong enough action.
Kean himself has already been fined 2,000 euros (£1,737) for diving during the game.
(Writing by Brian Homewood; Editing by Toby Davis)
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