The magnetic system of the Mn$_{1-x}$Fe$_{x}$Ge solid solution is ordered in a spiral spin structure in the whole concentration range of $x in [0 div 1]$. The close inspection of the small-angle neutron scattering data reveals the quantum phase transition from the long-range ordered (LRO) to short range ordered (SRO) helical structure upon increase of Fe-concentration at $x in [0.25 div 0.4]$. The SRO of the helical structure is identified as a Lorentzian contribution, while LRO is associated with the Gaussian contribution into the scattering profile function. The scenario of the quantum phase transition with $x$ as a driving parameter is similar to the thermal phase transition in pure MnGe. The quantum nature of the SRO is proved by the temperature independent correlation length of the helical structure at low and intermediate temperature ranges with remarkable decrease above certain temperature $T_Q$. We suggest the $x$-dependent modification of the effective Ruderman-Kittel-Kasuya-Yosida exchange interaction within the Heisenberg model of magnetism to explain the quantum critical regime in Mn$_{1-x}$Fe$_{x}$Ge.
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