The Welshman made an arm gesture after scoring his side's third goal and his 100th for the club in the 74th minute.
Bale raised his bent arm and hit it with his other hand, a gesture that is considered offensive in Spain.
He could face a ban if deemed to have intentionally incited opposition fans.
La Liga has expressed a desire to cut out "offensive goal celebrations" and it will be the task of the RFEF Competition Committee to decide whether or not to impose punishment.
A gesture made with intent that incites fans could be met with a ban of between four and 12 games, with a ban of up to three games applying for a gesture that is made with intent, but does not cause a hostile reaction.
Bale has been used sparingly in recent weeks by Real and fallen out of favour with some fans - an online poll by newspaper AS, suggested 54% did not want him to be in their starting line-up. However, he did start their most recent match - the 2-1 Champions League last-16 first-leg victory at Ajax.
Read More (...)