Di Maria appeared to grab his genitals after being whistled by the crowd at the Bernabeu as he was replaced by Gareth Bale with 25 minutes remaining.
However, the Argentine has denied there was any malice intended in the gesture and said he welcomed the opportunity to explain himself to the club's hierarchy.
Angel Di Maria. Pic/ AFP
"I made a normal gesture as I was leaving the field," he told the club's website.
"I didn't mean it to be aimed at the fans nor the coach as people are saying. It was a normal gesture that any man would do, especially when you are running.
"It seems correct to me (that the club are investigating). Not just for them to open the investigation, but also for me to explain to them the situation and what happened."
Di Maria has seen his first team opportunities limited since the arrival of Bale from Tottenham Hotspur in September.
The 25-year-old has been linked with a move away from Madrid in the January transfer window with free-spending Ligue 1 side Monaco reportedly interested.