A 10-

Context. To constrain present star formation models, we need to simultaneously establish the dynamical and physical properties of disks and jets around young stars. Aims. We previously observed the star-forming region G16.59−0.05 through interferometric observations of both thermal and maser lines, and identified a high-mass young stellar object (YSO) which is surrounded by an accretion disk and drives a nonthermal radio jet. Our goals are to establish the physical conditions of the environment hosting the high-mass YSO and to study the kinematics of the surrounding gas in detail. Methods. We performed high-angular-resolution (beam FWHM ≈ 0′′.15) 1.2-mm continuum and line observations towards G16.59−0.05 with the Atacama Large Millimeter Array (ALMA). Results. The main dust clump, with size ≈104 au, is resolved into four distinct, relatively compact (diameter ~2000 au) millimeter (mm) sources. The source harboring the high-mass YSO is the most prominent in molecular emission. By fitting the emission profiles of several unblended and optically thin transitions of CH3OCH3 and CH3OH, we derived gas temperatures inside the mm sources in the range 42–131 K, and calculated masses of 1–5 M⊙. A well-defined Local Standard of Rest (LSR) velocity (VLSR) gradient is detected in most of the high-density molecular tracers at the position of the high-mass YSO, pinpointed by compact 22-GHz free-free emission. This gradient is oriented along a direction forming a large (≈70°) angle with the radio jet, traced by elongated 13-GHz continuum emission. The butterfly-like shapes of the P–V plots and the linear pattern of the emission peaks of the molecular lines at high velocity confirm that this VLSR gradient is due to rotation of the gas in the disk surrounding the high-mass YSO. The disk radius is ≈500 au, and the VLSR distribution along the major axis of the disk is well reproduced by a Keplerian profile around a central mass of 10 ± 2 M⊙. The position of the YSO is offset by ≳0′′.1 from the axis of the radio jet and the dust emission peak. To explain this displacement we argue that the high-mass YSO could have moved from the center of the parental mm source owing to dynamical interaction with one or more companions