Double-beta decays of $^{100}\mathrm{Mo}$ from the 6.0195-year exposure of a 6.914 kg high-purity sample were recorded by the NEMO-3 experiment that searched for neutrinoless double-beta decays. These ultrarare transitions to $^{100}\mathrm{Ru}$ have a half-life of approximately $7\ifmmode\times\else\texttimes\fi{}{10}^{18}$ years and have been used to conduct the first-ever search for periodic variations of this decay mode. The Lomb-Scargle periodogram technique, and its error-weighted extension, were employed to look for periodic modulations of the half-life. Data show no evidence at the 95% confidence level of modulations with amplitude greater than 2.5% in the frequency range of $0.33225\phantom{\rule{4pt}{0ex}}{\mathrm{yr}}^{\ensuremath{-}1}$ to $360\phantom{\rule{4pt}{0ex}}{\mathrm{yr}}^{\ensuremath{-}1}$.
