We present the results of a study aimed at characterizing the kinematics of the inner regions of the halo globular cluster M75 (NGC 6864) based on data acquired as part of the ESO-VLT Multi-Instrument Kinematic Survey (MIKiS) of Galactic globular clusters. Our analysis includes the first determination of the line-of-sight velocity dispersion profile in the core region of M75. By using MUSE/NFM observations, we obtained a sample of ~1900 radial velocity measurements from individual stars located within 16" (corresponding to about r<3r_c_ where r_c_ is the estimated core radius of the system) from the cluster center. After an appropriate selection of the most accurate velocity measures, we determined the innermost portion of the velocity dispersion profile, finding that it is characterized by a constant behavior and a central velocity dispersion of {sigma}_0_~9km/s. The simultaneous King model fitting to the projected velocity dispersion and density profiles allowed us to check and update previous determinations of the main structural parameters of the system. We also detected a mild hint of rotation in the central ~7" from the center, with an amplitude of just ~1.0km/s and a position angle of the rotation axis of PA_0_=174deg. Intriguingly, the position angle is consistent with that previously quoted for the suspected rotation signal in the outer region of the cluster. Taking advantage of the high quality of the photometric catalog used for the analysis of the MUSE spectra, we also provide updated estimates of the cluster distance, age, and reddening.