Mourinho is being investigated by the Spanish football federation (RFEF) after he jabbed a finger into Tito Vilanova's eye during a mass brawl that flared up during last month's Spanish Super Cup match.
Cruyff, who coached Barca to four straight La Liga titles in the early 1990s, told Monday's El Periodico daily Mourinho's behaviour was damaging Real Madrid's image and was born of an obsession with beating Barca at any cost.
"Mourinho might be a very good person in private and a very good coach but the side he shows the world is something else," Cruyff said.
"Many people say that he does it to deflect attention so that it will be talked about and not the football," he added.
"I don't believe it. It is an act of arrogance and impotence."
Mourinho, who served as an assistant Barca coach in the late 90s, could be handed a lengthy ban by the federation and Cruyff said Real shared a responsibility to rein in the former Porto, Chelsea and Inter Milan manager.
"The current situation is extremely disagreeable," the Dutchman told El Periodico.
"Madrid's responsibility in the world is very great and there are certain things you should not allow to happen.
"There are millions of children in the world who have been showed a terrible example and Madrid is not looking out for them in any way. The club has the duty to change the situation.
"Madrid has always been great for many years due to the way it is, its style, its behaviour.
"Now, with every day that passes it's losing prestige. The problem now is that it is obsessed with Barca and it has gone beyond the limits."
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