Baena complained on Twitter on Sunday about being "attacked" and denied he had insulted Valverde's family, which some reports cite as the reason for the Uruguayan's anger.
"I'm very sad for the attack that I suffered after the game and surprised about what they are saying about me, it's totally false that I said that," wrote Baena on Twitter.
Real Madrid and Villarreal did not respond to requests for comment from AFP.
Villarreal beat Real Madrid 3-2 at the Santiago Bernabeu and after the game, Spanish reports state that Valverde waited by the visitors' team bus to confront Baena.
"Fede Valverde, thuggish and cowardly," Villarreal team delegate Xisco Nadal wrote on Twitter on Sunday, before later deleting his post.
Referee Javier Alberola Rojas did not include any reference to the incident in his report from the game.
Spanish newspaper Marca report that sources close to Valverde say Baena upset the Madrid player during the teams' Copa del Rey clash in January by speaking about his unborn child.
Valverde's partner Mina Bonino revealed in February the couple thought they had lost their baby, but the pregnancy was later found to be healthy.
Marca say Baena again referred to Valverde's child during the match on Saturday, provoking the confrontation.
