High-resolution infrared laser spectroscopy has been used to obtain rotationally resolved spectra of HCN-Zn-n (n = 1- 4) complexes formed in helium nanodroplets. In the present study the droplets passed through a metal oven, where the zinc vapor pressure was adjusted until one or more atoms were captured by the droplets. A second pickup cell was then used to dope the droplets with a single HCN molecule. Rotationally resolved infrared spectra are obtained for all of these complexes, providing valuable information concerning their structures. Stark spectra are reported and used to determine the corresponding permanent electric dipole moments. Ab initio calculations are also reported for these complexes for comparison with the experimental results.