"He died a few minutes ago. He did not survive the cardiac arrest and died in the intensive care unit," a spokeswoman for Madrid's Hospital Clinic told AFP. At least 11 other people were injured, emergency medics said.
Police confirmed that 24 people had been arrested in the incidents that took place in the streets parallel to the Manzanares river surrounding the Calderon.
Emergency services said that the 43-year-old, who is believed to be a Deportivo supporter, had also suffered hypothermia and head injuries after having to be rescued from the river by firefighters.
A police officer is among the 11 other people being treated for minor injuries.
Among those arrested are members of the Atletico and Deportivo ultra groups, Frente Atletico and Riazor Blues, as well ultras from the Bukaneros and Alkor Hooligans groups who follow Madrid-based sides Rayo Vallecano and Alcorcon.
Spanish minister for Culture, education and sport, Jose Ignacio Wert, has called a meeting with the anti-violence commission for Monday morning.
"The incidents we have seen today are the type of things we never want to see in sport," he said.
The presidents of both sides addressed the media following the match to condemn the violence.
"We cannot expand on the details because we don't know them and they are under investigation," said Atletico president Enrique Cerezo.
"I repeat that neither Atletico Madrid nor Deportivo have anything to do with these radical groups that have their own histories and stories."
Meanwhile, Deportivo president Tino Fernandez said the club would support the family of the deceased.
"We want to express that we strongly reject violence. At the moment we don't know the details and it is tragic news," he said.
"The clubs need to act so that these things don't happen anymore. Our position is well-known and we have to lament what has happened. We are at the disposition of the family."
Earlier the Spanish football league (LFP) claimed in a statement that they had tried to have the match postponed prior to kick-off.
"The LFP is repulsed by the incidents that took place on Sunday morning close to the Vicente Calderon stadium in the build up to the match between Atletico Madrid and Deportivo de La Coruna.
"The LFP was firm in its intention to suspend the game, but it wasn't possible. The institution is working alongside Fans United, the national police and all clubs to eradicate violence, racism, xenophobia and intolerance in professional football."