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
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