LaLiga has found "no evidence" that Cadiz's Juan Cala racially abused Valencia's Mouctar Diakhaby.
Play was halted during the first half of Sunday's clash between the sides following an altercation involving Cala and Diakhaby, after which the Valencia player and his team-mates left the pitch.
Diakhaby did not return for the remainder of the game, which resumed after a 20-minute delay, while Cala was substituted at half-time.
In a video posted on Twitter, Diakhaby said Cala called him "negro de mierda" which translates as "black s***".
Cala maintained his innocence at a subsequent news conference, insisting he had simply told Diakhaby to "leave me in peace".
The Spanish top-flight's governing body released a statement on Friday after concluding its investigation into the incident, which included the use of lip reading experts.
"After the analysis of the material, it is concluded that no evidence has been found... that the player Juan Torres Ruiz (Juan Cala) insulted Mouctar Diakhaby in the terms denounced," it read.
"Specifically, the audiovisual and digital files available have been examined, the audio of the meeting, the images broadcast and what was disseminated on the different social networks have been analysed.
"In order to complement the report, a specialised company has been hired, which has carried out a lip reading analysis of the conversations and a study of the behaviour of the players Juan Torres Ruiz and Mouctar Diakhaby.
"LaLiga has shared these reports with the clubs involved and the relevant authorities, so that they form part of those ongoing investigations.
"LaLiga reiterates its condemnation against racism in all its forms and maintains its commitment to permanently fight against any type of demonstration in this regard, which has materialised in the presentation of numerous complaints of hate crimes, including as a private accusation, in previous proceedings."
The Spanish Football Federation is also looking into the matter.