Aims. We present spatially resolved, high-spectral resolution K-band observations of the red supergiant Betelgeuse (α Ori) using AMBER at the Very Large Telescope Interferometer (VLTI). Our aim is to probe inhomogeneous structures in the dynamical atmosphere of Betelgeuse. Methods. Betelgeuse was observed in the wavelength range between 2.28 and 2.31 μm with VLTI/AMBER using baselines of 16, 32, and 48 m. The spectral resolutions of 4800−12 000 allow us to study inhomogeneities seen in the individual CO first overtone lines. Results. Spectrally dispersed interferograms have been successfully obtained in the second, third, and fifth lobes, which represents the highest spatial resolution (9 mas) achieved for Betelgeuse. This corresponds to five resolution elements over its stellar disk. The AMBER visibilities and closure phases in the K-band continuum can be reasonably fitted by a uniform disk with a diameter of 43.19 ± 0.03 mas or a limb-darkening disk with 43.56 ± 0.06 mas and a limb-darkening parameter of (1.2 ± 0.07) × 10 −1 . These AMBER data and the previous K-band interferometric data taken at various epochs suggest that Betelgeuse seen in the K-band continuum shows much smaller deviations from the above uniform disk or limb-darkened disk than predicted by recent 3-D convection simulations for red supergiants. On the other hand, our AMBER data in the CO lines reveal salient inhomogeneous structures. The visibilities and phases (closure phases, as well as differential phases representing asymmetry in lines with respect to the continuum) measured within the CO lines show that the blue and red wings originate in spatially distinct regions over the stellar disk, indicating an inhomogeneous velocity field that makes the star appear different in the blue and red wings. Our AMBER data in the CO lines can be roughly explained by a simple model, in which a patch of CO gas is moving outward or inward with velocities of 10−15 km s −1 , while the CO gas in the remaining region in the atmosphere is moving in the opposite direction at the same velocities. Also, the AMBER data are consistent with the presence of warm molecular layers (so-called MOLsphere) extending to ∼1.4−1.5 R with a CO column density of ∼1 × 10 20 cm −2 . Conclusions. Our AMBER observations of Betelgeuse are the first spatially resolved study of the so-called macroturbulence in a stellar atmosphere (photosphere and possibly MOLsphere as well) other than the Sun. The spatially resolved CO gas motion is likely to be related to convective motion in the upper atmosphere or intermittent mass ejections in clumps or arcs.