The origin of compact millimeter (mm) continuum emission from radio-quiet active galactic nuclei (RQAGNs) remains not fully understood. Changing-state AGNs (CSAGNs) exhibit rapid and strong variability, which allows us to investigate the origin of the mm emission. We present here the results of a first study of the mm continuum variability of a CSAGN using archival ALMA band 6 (∼230 GHz) observations of NGC 1566 obtained from 2014 to 2023. We find a positive correlation between the mm and X-ray flux with an intrinsic scatter of 0.05 dex (1σ), suggesting a common origin. The mm spectral index (αmm) is found to be in the range of 0.13±0.38 to – 0.26±0.53, consistent with a compact optically thick synchrotron source. No significant correlation was found between the αmm and the mm flux. The mm/X-ray ratio also shows no clear link to the Eddington ratio but is higher in the low-accretion state. We discuss several scenarios about the origin of the mm emission in NGC 1566. We find that synchrotron emission in the magnetized X-ray corona appears to be the most probable origin of the mm emission, confirming that mm emission can be used as a tracer of AGN activity in RQAGNs.