In this letter, a novel Beam Index Modulation (BIM) architecture with hybrid beamforming is introduced for millimeter-wave (mmWave) communications. Indeed, spatial scattering modulation and BIM have recently been proposed as a potential extension for Spatial Modulation to deal with sparse non Line of Sight channel environments. However, these recent approaches lack complete analyses for practical scenarios. SSM is limited to orthogonal non correlated channel paths and single user up-link scenarios, while BIM was hitherto studied for analog beamforming scenarios in which the interference between the beams is not tackled. Aiming at mitigating such inter-beam interference, we propose in this paper to add a digital precoding layer to the conventional analog-BIM framework, thus leading to a hybrid-BIM scheme. We analyze the performance of such new scheme by deriving the analytic closed form expressions of the achievable spectral efficiency and bit error probability. Simulation results show the validity of our theoretical results and highlight the performance gain brought by the hybrid beamforming strategy applied to BIM mmWave communications.