Combinations of III–V nanowires (NWs) with quantum dots (QDs) are promising building blocks for quantum light sources. Herein, for the first time, the results of growing AlGaAs NWs with InGaAs QDs by molecular-beam epitaxy on a silicon substrate are shown. The optimal growth temperature is determined and the physical properties of the grown nanostructures are studied. It is shown that the grown nanostructures exhibit photoluminescence (PL) signal up to room temperature in a wide wavelength range, including 1.3 μm emission which is important for the optical fiber transmission. It is found that in addition to InGaAs QDs radial InGaAs quantum wells are formed inside the NWs as a result of lateral/axial InGaAs growth competition. The proposed technology opens up new possibilities for the integration of direct-band III–V materials with the silicon platform for various applications in the field of silicon photonics and quantum communication technology.