Atletico accused Barcelona of approaching the Argentine, whose contract runs until June 2030, without first notifying them in writing.
The sanction falls under Article 133 of the federation's regulations. Atletico also complained to FIFA, which declared it had no jurisdiction over the case.
For Alvarez, the repair work has been rather more public.
The striker scored Atletico's winner against Deportivo La Coruna on Saturday, finding the net for a second successive match as his side moved within two points of LaLiga leaders Barcelona, before apologising for expressing his desire to join their rivals.
"It was a mistake. I understand why the fans are angry. If I were a fan, I'd be angry too. Especially given how they've supported me since I arrived," Alvarez said referring to an interview during the 2026 World Cup in which he said that he "wanted to fulfil his dream" of playing for Barcelona, triggering a transfer dispute that stretched through the summer transfer window.
Frequently booed by the home fans this season, Alvarez received a standing ovation from sections of the crowd after scoring on Saturday, a sign of a thawing relationship with the Metropolitano faithful.