The prompt $\ensuremath{\gamma}$-ray energy and multiplicity distributions were measured for the neutron-induced fission in ${}^{235}\mathrm{U}$ and ${}^{239,241}\mathrm{Pu}$ by using a highly segmented $4\ensuremath{\pi}\phantom{\rule{0.28em}{0ex}}\ensuremath{\gamma}$-ray calorimeter in coincidence with the detection of fission fragments by a gas-filled parallel-plate avalanche counter. Both distributions were unfolded according to the detector response, which was simulated numerically by using a model validated with the $\ensuremath{\gamma}$-ray calibration sources. The mean value and the width of the $\ensuremath{\gamma}$-ray multiplicity distribution show a systematic increase with increasing mass of fissile nucleus, whereas, the energy distribution shows the dependence of $\ensuremath{\gamma}$-ray energy above 5 MeV on the species of fissile nuclei. The correlations between $\ensuremath{\gamma}$-ray energy and multiplicity were studied by comparing the mean value and the width of the total $\ensuremath{\gamma}$-ray energy between measurement and simulation by using an assembly with elements selected by random sampling of their unfolded distributions. The detector response was taken into account in the simulation. These results together with the detailed description of the experiment and analysis are presented.