We report the detection of a potential quasi-periodic signal with a period of $\sim$2 yr in the blazar ON 246, based on Fermi-LAT ($\gamma$-rays) and ASAS-SN (optical) observations spanning 11.5 yr (MJD 55932–60081). We applied various techniques to investigate periodic signatures in the light curves, including the Lomb-Scargle periodogram (LSP), weighted wavelet Z-transform (WWZ), and REDFIT. The significance of the signals detected in LSP and WWZ was assessed using two independent approaches: Monte Carlo simulations and red noise modelling. Our analysis revealed a dominant peak in the $\gamma$-ray and optical light curves, with a significance level exceeding 3$\sigma$ in both LSP and WWZ, consistently persisting throughout the observation period. Additionally, the REDFIT analysis confirmed the presence of a quasi-periodic signal at $\sim$0.00134 day$^{-1}$ with a 99$\%$ confidence threshold. To explain the observed quasi-periodic variations in $\gamma$-ray and optical emissions, we explored various potential physical mechanisms. Our analysis suggests that the detected periodicity could originate from a supermassive binary black hole (SMBBH) system or the jet-induced orbital motion within such a system. Based on variability characteristics, we estimated the black hole mass of ON 246. The study suggests that the mass lies within the range of approximately $(0.142 - 8.22) \times 10^9$ M$_{\odot}$.