We study the mass-metallicity relation for 19 members of a spectroscopically-confirmed protocluster in the COSMOS field at $z=2.2$ (CC2.2), and compare it with that of 24 similarly selected field galaxies at the same redshift. Both samples are $\rm H\alpha$ emitting sources, chosen from the HiZELS narrow-band survey, with metallicities derived from $\rm N2\ (\frac{\rm [NII] \lambda 6584}{\rm H \alpha})$ line ratio. For the mass-matched samples of protocluster and field galaxies, we find that protocluster galaxies with $10^{9.9} \rm M_\odot \leq M_* \leq 10^{10.9} \rm M_\odot$ are metal deficient by $0.10 \pm 0.04$ dex ($2.5\sigma$ significance) compared to their coeval field galaxies. This metal deficiency is absent for low mass galaxies, $\rm M_* <10^{9.9} \rm M_\odot$. Moreover, relying on both SED-derived and $\rm {H\alpha}$ (corrected for dust extinction based on $\rm {M_*}$) SFRs, we find no strong environmental dependence of SFR-$\rm {M_*}$ relation, however, we are not able to rule out the existence of small dependence due to inherent uncertainties in both SFR estimators. The existence of $2.5\sigma$ significant metal deficiency for massive protocluster galaxies favors a model in which funneling of the primordial cold gas through filaments dilutes the metal content of protoclusters at high redshifts ($z \gtrsim 2$). At these redshifts, gas reservoirs in filaments are dense enough to cool down rapidly and fall into the potential well of the protocluster to lower the gas-phase metallicity of galaxies. Moreover, part of this metal deficiency could be originated from galaxy interactions which are more prevalent in dense environments.