Valverde was a second-half substitute in what proved to be a 3-2 home loss for Los Blancos, while Baena played 91 minutes of the clash for Villarreal before being substituted in the final moments.
According to ESPN, there was an incident in the car park after the league match, with Valverde punching Baena after a remark from the latter about the former's unborn child.
The report claims that Baena had made the comment during the match, and Valverde then waited for him in the stadium's car park in order to confront him.
"Fede never has problems with anyone and this has been due to something very serious that comes from before," the midfielder's representatives told Marca.
Baena allegedly first made comments regarding Valverde's unborn child in the Copa del Rey contest between Villarreal and Real Madrid earlier this year.
Valverde alleges that another remark was made on Saturday evening during the league game, which led to him confronting Baena by Villarreal's team bus.
The midfielder's partner Mina Bonino has taken to Twitter to comment on the situation, with the pair initially being told that their unborn child's health was at serious risk before learning that it was a healthy pregnancy.
"I have to go out and give explanations of when they told me that my pregnancy could not continue? We were silent for almost two months, waiting for the results to know if we could continue or not, having already undergone FIVE months of gestation," she wrote on her social media.
"In spite of everything, from my heart, I do not wish anyone to have to go through a similar situation. It's the last thing I wish to be put in, but for me it's torture to relive this. I understand that it was already public that something was happening with my pregnancy."
According to AS, neither Villarreal nor Baena are preparing to report the incident, which will see Valverde escape what could have been a lengthy ban.
However, Valverde could yet face a criminal charge of assault, with the decision up to Baena whether he will press charges against the Uruguay international.
Real Madrid led 1-0 and 2-1 during Saturday's affair but ultimately suffered a 3-2 loss, with Jose Luis Morales levelling for the Yellow Submarine before Samuel Chukwueze netted his second late on.