We present the preparation and measurements of nanowires of single-crystal NbSe$_2$. These nanowires were prepared on ultrathin ($lesssim10text{ nm}$) flakes of NbSe$_2$ mechanically exfoliated from a bulk single crystal using a process combining electron beam lithography and reactive plasma etching. The electrical contacts to the nanowires were prepared using Ti/Au. Our technique, which overcomes several limitations of methods developed previously for fabricating superconducting nanowires, also allows for the preparation of complex superconducting nanostructures with a desired geometry. Current-voltage characteristics of individual superconducting single-crystal nanowires with widths down to 30~nm and cross-sectional areas as low as 270 nm$^2$ were measured for the first time.