The supporters were revelling in the centre of the northern Italian city on Tuesday evening after Morocco's victory over Spain when they were attacked by a group of men dressed in black with their faces covered, the police said in a statement.
Those held "were identified by investigators as militants of far-right groups in the city," the statement said.
Morocco's World Cup progress has seen vibrant celebrations by its supporters in cities with large Moroccan immigrant populations around the world, which have sometimes turned violent.
Their victory over Belgium in the group stage sparked riots in Brussels, and on Tuesday evening video footage showed fans lighting flares and throwing furniture and other objects in the centre of Milan.
Italy's Deputy Prime Minister Matteo Salvini, leader of the anti-immigrant League party, tweeted the images of the Milan episodes, saying he hoped those responsible would be identified and made to pay for the damage to property.
He did not comment on the incidents in Verona.