  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.
