Quercetin (Que) has garnered attention as a flavonoid that exhibits various biological activities, such as antioxidant and anti-inflammatory effects; however, its solubility must be improved. In this study, we attempt to improve the solubility of Que by preparing a co-amorphous Que with an amino acid (i.e., β-alanine (Ala) and L-arginine (Arg)) via a mechanochemical process. After grinding, the samples are characterized using powder X-ray diffraction, differential scanning calorimetry, electron spin resonance, and ultraviolet–visible spectroscopy. Discrete element method simulations are performed to evaluate the amorphization progress following the energy predicted from ball impact. The amorphization of Que–Ala samples progresses with milling, whereas Que–Arg is converted to be co-amorphized by milling in addition to the arginine-assisted solubilizing effect. The number of radicals and the solubility of Que–Arg are much higher than those of Que–Ala, indicating that the antioxidant capacity of Que–Arg is enhanced by co-amorphization. The number of radicals increases with the rotational speed of grinding, and the solubility of Que increases similarly, suggesting that the number of radicals may exert a positive solubility effect on Que. This co-amorphous strategy via a mechanochemical process can enhance the solubility and antioxidant capacity of other polyphenols.