The recent experimental realization of chromium Bose-Einstein condensates has encouraged research on the new field of dipolar gases at very low temperature. While the $s$-wave contact interaction is isotropic, the dipolar interaction is anisotropic and long-range, giving rise to interesting phenomena in dipolar condensates. These gases constitute a unique testing ground of the interplay between different interatomic interactions in the superfluid properties, in particular in quantized vortex states. We investigate the properties of a singly quantized vortex and calculate the critical angular velocity for different values of the s-wave scattering length. The energy barrier for the nucleation of a vortex is calculated as a function of the vortex displacement from the rotation axis.