The football club known informally as Atleti have stripped Frente Atlético of official fan club status, it announced on Tuesday.
It will now use "all means within its power" to stop banners or other distinctive paraphernalia associated with the group from being displayed in its home ground, the Vicente Calderón.
The club has now identified 15 members of the 'ultra', or extremist, group involved in Sunday's brawl with fans of Galician football club Deportivo La Coruña which lead to the death of a Deportivo fan.
Seven of those people were members of the club and have now been stripped of their membership and face a lifetime ban, Atlético Madrid said.
Deportivo La Coruña, meanwhile, have announced that the section of the stands where their ultra fans congregate will be closed for the team's next two home matches to show the club's lack of tolerance of violent fans.
The move comes after authorities said they would come down hard on clubs that did not take strong action against hooligan fans in the wake of Sunday's death.
While authorities described Sunday's events as "exceptional", they described them as "extremely serious".
Twenty-one arrests have been made to date in connection to the brawl, but none of the people detained have been charged with homicide and further arrests are expected.
Police sources said the trouble on Sunday started after rioters from La Coruna travelled in a coach hired in a different city to avoid being identified as Deportivo fans.
The rival groups arranged to meet for their brawl by exchanging messages on WhatsApp, a mobile telephone application that is less easy to monitor than other online social networks.
Police had categorized Sunday's match as low-risk since there had not been any incidents between fans of the two sides in the past six years, officials said.
Of the 21 people in detention on Monday, four were from Frente Atlético, a group linked to fans of the Spanish league champions, and 14 from Riazor Blues, a police spokesman told news agency AFP.
One was from the Alcorcon group Alkor Hooligans and two from the Bukaneros of Vallecas.
The two latter groups are considered politically extreme-left and are thought to have teamed up with Riazor Blues to fight against the far-right Frente Atlético.
"These groups meet up and form alliances. They do not act according to their sporting allegiances but rather to their ideological affinities," said Miguel Cardenal, Spain's junior sports minister.
Spain's opposition Socialist Party demanded that Interior Minister Jorge Fernández Diaz face questions in parliament about the level of police surveillance in Madrid on Sunday.
The BNG nationalist party from the Galicia region where La Coruna is located also demanded an explanation, alleging an absence of police ahead of the match.
"What happened was absolutely deplorable," said Spain's Prime Minister Mariano Rajoy on Monday, speaking during a visit to Paris.
"It is very important that everyone — government, clubs and the media — get involved" in solving the problem, he added.
"Some clubs have made an effort by themselves to eradicate such behaviour," he said, alluding to Real Madrid and Barcelona.
Barcelona in 2003 banned the Boixos Nois radical fan group and last January Real Madrid did the same to members of the extremist collective Ultrasur.
Cardenal said authorities were considering possible sanctions such as partially closing stadia or banning radical groups from them.
In 2003 a Deportivo fan died after being beaten by radical fans of his own team as he tried to protect a boy wearing a rival side's shirt.
A Real Sociedad fan, Aitor Zabaleta, died after being stabbed near the Calderon stadium prior to a match in December, 1998. A right-wing Atlético radical was jailed for his murder.