We propose a new insight into the mechanism of low-temperature Au-assisted growth of InAs nanowires during molecular beam epitaxy (MBE). The nanowire MBE growth was achieved at a temperature of 270 °C on both Si(111) and SiC/Si(111) substrates. A special procedure of substrate preparation was used to obtain a high yield of nanowires grown perpendicularly to the substrate. The morphology of the InAs nanowire array was studied by scanning electron microscopy (SEM) revealing a significantly higher percentage of vertical InAs nanowires compared with previous works. The structural properties of nanowires and the catalyst composition were investigated by analytical methods of transmission electron microscopy (TEM). A theoretical assessment of the growth of InAs nanowires in the frame of the classical nucleation theory has shown the possibility of vapor-solid-solid growth at extremely low temperature, e.g., at 270 °C. It was found that the presence of elastic stresses due to the lattice mismatch between the solid catalyst particle and the nanowire material influences the nanowire growth rate. This important feature of nucleation in solid in the case of vapor-solid-solid growth of III-V nanowires was investigated for the first time. Also, we have shown that the material transport of arsenic towards the interface between the catalyst particle and the nanowire top limits the nanowire growth rate. Further development of the low-temperature growth methods facilitates the integration of III-V semiconductors with silicon electronics.