In the context of a project aimed at characterizing the properties of star clusters in the Galactic bulge, here we present the determination of the internal kinematics and structure of the massive globular cluster NGC 6569. The kinematics has been studied by means of an unprecedented spectroscopic data set acquired in the context of the ESO-VLT Multi-Instrument Kinematic Survey of Galactic globular clusters, combining the observations from four different spectrographs. We measured the line-of-sight velocity of a sample of almost 1300 stars distributed between ~0.8" and 770" from the cluster center. From a subsample of high-quality measures, we determined the velocity dispersion profile of the system over its entire radial extension (from ~5" to ~200" from the center), finding the characteristic behavior usually observed in globular clusters, with a constant inner plateau and a declining trend at larger radii. The projected density profile of the cluster has been obtained from resolved star counts, by combining high-resolution photometric data in the center, and the Gaia EDR3 catalog radially extended out to ~20'for a proper sampling of the Galactic field background. The two profiles are properly reproduced by the same King model, from which we estimated updated values of the central velocity dispersion, main structural parameters (such as the King concentration, the core, half mass, and tidal radii), total mass, and relaxation times. Our analysis also reveals a hint of ordered rotation in an intermediate region of the cluster (40"<r<90", corresponding to 2r_c_<r<4.5r_c_), but additional data are required to properly assess this possibility.