The ex-Manchester United forward appeared to urge Barcelona fans to calm down after making it 1-1.
Spanish league (LFP) president Javier Tebas says they will investigate as they are keen to clamp down on provocative actions.
The policy follows the death of a Deportivo La Coruna fan in fighting before a league match in November.
"We have to be careful with provocative gestures by a player or conduct that could incite violence among spectators," said Tebas.
"It must be sanctioned, from a fine up to a suspension. We will look into it."
Barcelona went on to win the match 2-1 with Luis Suarez scoring the winner.
Cristiano Ronaldo appears to tell Barcelona fans to "calm down" as team-mates celebrate
Cristiano Ronaldo looks towards the Barcelona fans following his "calm down" gesture
Download the Howwe Music App
Deportivo La CorunaManchester UnitedBarcelona fansRonaldo may be punished for Clasico celebCristiano Ronaldo faces probe over goal celebrationSports