"While I have received a great amount of support… to continue my campaign, after a profound reflection I have decided to withdraw my bid," Villar said in statement posted on RFEF website.
Dutch football boss Michael van Praag and Slovenian FA chief Aleksander Ceferin remain the only contestants for the post.
The election has been set for September 14 at an Extraordinary UEFA Congress in Athens.
Former UEFA President Michel Platini and former FIFA President Joseph Blatter were both handed 8-year suspensions last December for their role in a major FIFA corruption scandal. It erupted after Swiss authorities opened a criminal case against Blatter in September 2015 over a payment of 2 million Swiss francs ($2.03 million at current exchange rates) that he made to Platini. However, later, Platini’s ban was reduced to four years.