There is a controversy about the extent to which the primary and secondary dielectric relaxations influence the crystallization of amorphous organic compounds below the glass transition temperature. Recent studies also point to the importance of fast molecular dynamics on picosecond-to-nanosecond time scales with respect to the glass stability. In the present study we provide terahertz spectroscopy evidence on the crystallization of amorphous naproxen well below its glass transition temperature and confirm the direct role of Johari–Goldstein (JG) secondary relaxation as a facilitator of the crystallization. We determine the onset temperature T_β above which the JG relaxation contributes to the fast molecular dynamics and analytically quantify the level of this contribution. We then show there is a strong correlation between the increase in the fast molecular dynamics and onset of crystallization in several chosen amorphous drugs. We believe that this technique has immediate applications to quantify the stability of amorphous drug materials.