Detecting nanomechanical motion has become an important challenge in Science and Technology. Recently, electromechanical coupling to focused electron beams has emerged as a promising method adapted to ultra-low scale systems. However the fundamental measurement processes associated with such complex interaction remain to be explored. Here we report highly sensitive detection of the Brownian motion of µm-long semiconducting nanowires (InAs). The measurement imprecision is found to be set by the shot noise of the secondary electrons generated along the electromechanical interaction. By carefully analysing the nano-electromechanical dynamics, we demonstrate the existence of a radial backaction process which we identify as originating from the momentum exchange between the electron beam and the nanomechanical device, which is also known as radiation pressure.