Impurity scattering in a superconductor may serve as an important probe for the nature of superconducting pairing state. Here we report the impurity effect on superconducting transition temperature $T_mathrm{c}$ in the newly discovered Cr-based superconductor K$_2$Cr$_3$As$_3$. The resistivity measurements show that the crystals prepared using high-purity Cr metal ($geq$99.99%) have an electron mean free path much larger than the superconducting coherence length. For the crystals prepared using impure Cr that contains various emph{nonmagnetic} impurities, however, the $T_mathrm{c}$ decreases significantly, in accordance with the generalized Abrikosov-Gorkov pair-breaking theory. This finding supports a non-$s$-wave superconductivity in K$_2$Cr$_3$As$_3$.
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