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The presence of nuclear magnetic resonance can be detected noninductively by coupling the nuclear spin to the motion of a mechanical oscillator. The coupling is obtained by applying a large-gradient magnetic field, which exerts a mechanical force on the particle by virtue of its magnetic moment. The coupling increases in strength as the oscillator mass is decreased and the gradient length scale is made shorter. Oscillator-based detection is thus only marginally effective for macroscopic samples, but can be quite effective for single protons interacting with a micron-scale oscillator. This letter describes the physics of devices in which single-nucleon magnetic resonance is detected by monitoring the excitation of a mechanical oscillator.