In nitride ternary alloys, natural compositional disorder induces strong electronic localization effects. We present a new experimental approach which allows a direct probing at nanometer scale of disorder-induced localization effects in InGaN/GaN quantum wells (QWs). In this experiment, samples are p-type heterostructures incorporating an InGaN/GaN QW nearby the surface. The electrons are locally injected from a scanning tunneling microscope (STM) tip into the conduction band of the thin cladding top GaN layer and captured in the InGaN QW where they radiatively recombine. The injected current is maintained constant by the STM feedback loop and the injection electron energy is controlled by the bias voltage applied to the tip-sample tunnel junction. The luminescence onset voltage coincides with electron injection above the bottom of the conduction band in the bulk GaN (beyond the band bending region). Thereby, scanning the tip allows the high-resolution mapping of the luminescence process in the InGaN QW. Spatial fluctuations of the luminescence peak energy and linewidth are observed on the scale of a few nanometers, which are characteristic of disorder-induced carrier localization. A model based on the so-called localization landscape theory is developed to take into account the effect of alloy disorder into simulations of the structure properties. The localization landscape notably describes an effective confining potential, whose basins and crests define the localization regions of carriers. This theory accounts well for the observed nanometer scale carrier localization and the energy-dependent luminescence linewidth observed for the quantum electron states in the disordered energy band.