Medium-spin excited states of the neutron-rich nucleus $^{87}$Br were observed and studied for the first time. They were populated in fission of $^{235}$U induced by the cold-neutron beam of the PF1B facility of the Institut Laue-Langevin, Grenoble. The measurement of $gamma$ radiation following fission has been 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 band-like structures, which can be understood as bands built on the ${pi}f_{5/2}$, ${pi}(p_{3/2}+f_{5/2})$ and ${pi}g_{9/2}$ configurations. The behavior of the observed ${pi}g_{9/2}$ 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 ${pi}g_{9/2}$ high-$it j$ proton polarizes the core.