Medium-spin excited states of the neutron-rich nucleus $^{87}\mathrm{Br}$ were observed and studied for the first time. They were populated in fission of $^{235}\mathrm{U}$ induced by the cold-neutron beam of the PF1B facility of the Institut Laue-Langevin, Grenoble. The measurement of $\ensuremath{\gamma}$ radiation following fission was performed using the EXILL array of Ge detectors. The observed level scheme was compared with results of large valence space shell model calculations. The medium-spin level scheme consists of three bandlike structures, which can be understood as bands built on the $\ensuremath{\pi}{f}_{5/2}$, $\ensuremath{\pi}({p}_{3/2}+{f}_{5/2})$, and $\ensuremath{\pi}{g}_{9/2}$ configurations. The behavior of the observed $\ensuremath{\pi}{g}_{9/2}$ band at high spins shows a considerable deviation from the shell model predictions. This deviation in this band is probably the result of an increased collectivity, which can be understood assuming that the $\ensuremath{\pi}{g}_{9/2}$ high-$\mathit{j}$ proton polarizes the core.