There are now hundreds of publicly available supernova spectral time series. Radiative transfer modeling of this data provides insight into the physical properties of these explosions, such as the composition, the density structure, and the intrinsic luminosity, which is invaluable for understanding the supernova progenitors, the explosion mechanism, and for constraining the supernova distance. However, a detailed parameter study of the available data has been out of reach due to the high dimensionality of the problem coupled with the still significant computational expense. We tackle this issue through the use of machine-learning emulators, which are algorithms for high-dimensional interpolation. These use a pre-calculated training dataset to mimic the output of a complex code but with run times that are orders of magnitude shorter. We present the application of such an emulator to synthetic type II supernova spectra generated with the TARDIS radiative transfer code. The results show that with a relatively small training set of 780 spectra we can generate emulated spectra with interpolation uncertainties of less than one percent. We demonstrate the utility of this method by automatic spectral fitting of two well-known type IIP supernovae; as an exemplary application, we determine the supernova distances from the spectral fits using the tailored-expanding-photosphere method. We compare our results to previous studies and find good agreement. This suggests that emulation of TARDIS spectra can likely be used to perform automatic and detailed analysis of many transient classes putting the analysis of large data repositories within reach.