Here we comprehensively investigate Landau levels, Hofstadter's butterfly, and transport properties of a semi-Dirac nanoribbon in a perpendicular magnetic field using a recently developed real-space implementation of the Kubo formula based on the kernel polynomial method. A Dirac ribbon is considered to compare and contrast our results for a semi-Dirac system. We find that with the Landau levels being nonequidistant from each other for the semi-Dirac case (which is true for a Dirac case as well), the flatness of the energy bands vanishes in the bulk and becomes dispersive for a semi-Dirac ribbon in contrast to a Dirac system. This feature is most discernible for intermediate values of the external field. We further compute the longitudinal (sigma(xx) and sigma(yy)) and the transverse or Hall (sigma(xy)) conductivities, where the Hall conductivity shows a familiar quantization, namely, sigma(xy) proportional to 2n (the factor of 2 includes the spin degeneracy), which is highly distinct from a Dirac system, such as graphene. We also observe anisotropic behavior in magnetotransport in a semi-Dirac ribbon owing to the dispersion anomalies in two different longitudinal directions. Our studies may have important ramifications for monolayer phosphorene.