We demonstrate a silicon carbide (SiC) zipper photonic crystal optomechanical cavity. The device is on a 3C-SiC-on-silicon platform and has a compact footprint of ∼30 × 1 μm. The device shows an optical quality of 2800 at telecom and a mechanical quality of 9700 at 12 MHz with an effective mass of ∼3.76 pg. The optical mode and mechanical mode exhibit strong nonlinear interaction, namely, the quadratic spring effect, with a nonlinear spring constant of 3.3 × 104 MHz2/nm. The SiC zipper cavity is potentially useful in sensing and metrology in harsh environments.