Hexagonal boron nitride (hBN) is an emerging layered material that plays a key role in a variety of two-dimensional devices, and has potential applications in nanophotonics and nanomechanics. Here, we demonstrate the first cavity optomechanical system incorporating hBN. Nanomechanical resonators consisting of hBN beams with predicted thickness between 8 nm and 51 nm were fabricated using electron beam induced etching and positioned in the optical nearfield of silicon microdisk cavities. A 160 fm/$sqrt{text{Hz}}$ sensitivity to the hBN nanobeam motion is demonstrated, allowing observation of thermally driven mechanical resonances with frequencies between 1 and 23 MHz, and mechanical quality factors reaching 1100 at room temperature in high vacuum. In addition, the role of air damping is studied via pressure dependent measurements. Our results constitute an important step towards realizing integrated optomechanical circuits employing hBN.