Electro-optic frequency combs were employed to rapidly interrogate an optomechanical sensor, demonstrating spectral resolution substantially exceeding that possible with a mode-locked frequency comb. Frequency combs were generated using an integrated-circuit-based direct digital synthesizer and utilized in a self-heterodyne configuration. Unlike approaches based upon laser locking or sweeping, the present approach allows rapid, parallel measurements of full optical cavity modes, large dynamic range of sensor displacement, and acquisition across a wide frequency range between DC and 500 kHz. In addition to being well suited to measurements of cavity optomechanical sensors, this optical frequency comb-based approach can be utilized for interrogation in a wide range of physical and chemical sensors.