The banners were reportedly unfurled during Juve's 1-0 win over Torino at the Juventus Stadium on Sunday, and are thought to have referenced a plane crash that occurred in 1949 when several Torino players, staff and journalists on board died.
Juventus were punished for a similar incident in 2012, for which the club received a €10,000 fine.
Agnelli has now warned supporters over their conduct and pleaded for fans not to reference the tragedy.
"Tragedies are not to be touched upon," he said in a statement on the club's official Twitter account.
"No more vile chants or banners. From anyone."
The incident has taken the shine off Juve's victory over their rivals, which was settled by Carlos Tevez's strike as the hosts regained their nine-point lead at the top of Serie A.
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