The 78-year-old, who is also known for his staunch opposition to Catalan separatism, is recovering in a Madrid hospital having survived the shooting as the bullet passed through his jaw.
After the attack, which took place in broad daylight, the motorcycle used by the gunman and his accomplice was found partially burned in a suburban area south of the capital.
Investigators were able to trace the vehicle, reportedly leading to the individual arrested in Fuengirola.
The man arrested in Lanjarón is believed to have ridden the motorcycle, and at least one of the two men detained has reportedly been identified on CCTV camera footage frequenting the scene of the shooting in the days prior to the attack.