LaLiga on Monday condemned threats and intimidation by Sevilla fans aimed at their own players and directors after they fell to a third straight league defeat.
Sevilla, 17th in the Spanish top flight, lost 1-0 away at bottom side Real Oviedo on Sunday and some supporters met the team at the airport on their return to insult them, while others wearing masks were at the club training ground.
LaLiga said in a statement this behaviour "unacceptably crosses the line of legitimate criticism and sporting expression".
Earlier this season, some Sevilla fans tried to force their way into the training ground to remonstrate with the players.
LaLiga said they would report the incident to Spanish authorities and continue to take action in the future against similar incidents.
"Anyone who crosses the line from criticism into threats, intimidation, or harassment stops acting as a fan and starts acting as a violent individual," added LaLiga. "And against violent individuals, LaLiga acts and will act."
Sevilla, winless in five matches, are two points above the relegation zone with eight games remaining in the season.