Recent advances in the fabrication of microelectromechanical systems (MEMS) and their evolution into nanoelectromechanical systems (NEMS) have allowed researchers to measure extremely small forces, masses, and displacements. In particular, researchers have developed position transducers with resolution approaching the uncertainty limit set by quantum mechanics. The achievement of such resolution has implications not only for the detection of quantum behavior in mechanical systems, but also for a variety of other precision experiments including the bounding of deviations from Newtonian gravity at short distances and the measurement of single spins. Here we demonstrate the use of a quantum point contact (QPC) as a sensitive displacement detector capable of sensing the low-temperature thermal motion of a nearby micromechanical cantilever. Advantages of this approach include versatility due to its off-board design, compatibility with nanoscale oscillators, and, with further development, the potential to achieve quantum limited displacement detection.