We describe a simple approach to detect small mechanical displacements by scattering evanescent optical waves confined around an optical waveguide. Our experimental setup consists of a microcantilever brought into the proximity of a tapered optical fiber. The scattering of evanescent waves and hence the optical transmission through the tapered fiber is strongly dependent on the separation between the fiber and the microcantilever, allowing for sensitive detection of the small oscillations of the microcantilever. Our approach does not require a coherent laser source, yet it provides a displacement sensitivity of ~ $260\mathrm{fm}{\mathrm{Hz}}^{-1/2}$ at a small power level of $38\mathrm{\mu W}$ . It is suitable for scanning probe microscopy and could eventually be adapted to nanomechanical resonators.