In the paper, we present the use of various models based on standard algorithms, ensemble methods, and neural networks for the fast prediction of the optical properties of nanostructured fibers. Such fibers are fabricated from several thousand elements, the spatial distribution of which determines the optical properties of the fiber. We show how to build a training set for a given class of nanostructured fibers and how different machine learning algorithms handle the estimation of a specific optical parameter. As a predicted parameter, we chose the zero dispersion wavelength, which is non-trivially dependent on the refractive index distribution in the fiber core. This approach allows for skipping time-consuming physical simulations and allows rapid verification of the properties of new fibers.