Pictures spread on social media showed a mannequin, wearing a Vinicius shirt, hung by the neck from a bridge in the Spanish capital.
A banner in the colours of Atletico was displayed on the same bridge which read: "Madrid hates Real".
In a statement, Atletico said: "Such acts are absolutely repugnant and inadmissible and shame society. Our condemnation of any act that attacks the dignity of persons or institutions is categorical and unreserved.
"The rivalry between the two clubs is the greatest, but so is respect. No individual, whatever their intentions or colours, can tarnish the coexistence between different supporters. It is everyone's responsibility to avoid this.
"We do not know the perpetrator or perpetrators of this despicable act, but their anonymity does not avoid their responsibility. We hope that the authorities succeed in clarifying what happened and that justice helps to banish this type of behaviour."
LaLiga also issued a statement on the matter, calling for a full investigation to be launched and criminal sanctions issued against guilty parties.
"We strongly condemn the acts of hatred directed towards Vinicius Junior. Intolerance and violence has no place in football," the statement read.
"As it has done before, La Liga will press for a full investigation in search of the facts and the conviction of those responsible, requesting the most severe criminal sanctions."
It is not the first time Vinicius has been targeted by sections of the Atletico fanbase, with footage outside the Civitas Metropolitano ahead of the LaLiga clash between the two clubs earlier this season showing fans chanting abuse.
Madrid have now joined their neighbours in condemning what they label as a "repugnant act of racism, xenophobia and hatred".
A statement read: "Real Madrid would like to thank you for the support and expressions of affection received after the regrettable and repugnant act of racism, xenophobia and hatred against our player Vinicius.
"We would like to express our strongest condemnation of these acts which are an attack on fundamental rights and the dignity of people, and which have nothing to do with the values that football and sport represent.
"Attacks such as those suffered by our player, or those suffered by any sportsperson, have no place in a society such as ours
"Real Madrid trust that those who have participated in such a despicable act will be held accountable."
The Confederacao Brasileira de Futebol (CBF) also joined in the condemnation.
"The CBF vehemently repudiates the racist acts suffered once again by Vinicius," a statement read.
"Intolerance and discrimination are not part of sport and must be eliminated from society. We hope that those responsible are identified and punished under the law."
LaLiga called for a full investigation to be launched and criminal sanctions issued against guilty parties.
