Luminous BA-type supergiants are the brightest stars in the visible that can be observed in distant galaxies and are potentially accurate distance indicators. The impact of the variability of the stellar winds on the distance determination remains poorly understood. Our aim is to probe the inhomogeneous structures in the stellar wind using spectro-interferometric monitoring. We present a spatially resolved, high-spectral resolution (R=12000) K-band temporal monitoring of the bright supergiant {beta} Orionis (Rigel, B8 Iab) using Amber at the Very Large Telescope Interferometer (VLTI). Rigel was observed in the Br{gamma} line and its nearby continuum once per month over 3 months in 2006-2007, and 5 months in 2009-2010. These unprecedented observations were complemented by contemporaneous optical high-resolution spectroscopy. We analyse the near-IR spectra and visibilities with the 1D non-LTE radiative-transfer code CMFGEN. The differential and closure phase signals are evidence of asymmetries that are interpreted as perturbations of the wind.