Context. Temporal variability in the photometric and spectroscopic properties of protoplanetary disks is common in young stellar objects. However, evidence pointing toward changes in their morphology over short timescales has only been found for a few sources, mainly due to a lack of high-cadence observations at high angular resolution. Understanding this type of variation could be important for our understanding of phenomena related to disk evolution. Aims. We study the morphological variability of the innermost circumstellar environment of HD 98922, focusing on its dust and gas content. Methods. Multi-epoch observations of HD 98922 at milliarcsecond resolution with VLTI/GRAVITY in the K-band at low (R = 20) and high (R = 4000) spectral resolution are combined with VLTI/PIONIER archival data covering a total time span of 11 yr. We interpret the interferometric visibilities and spectral energy distribution with geometrical models and through radiative transfer techniques using the code MCMax. We investigated high-spectral-resolution quantities (visibilities and differential phases) to obtain information on the properties of the HI Brackett-γ (Brγ)-line-emitting region. Results. Comparing observations taken with similar (u,v) plane coverage, we find that the squared visibilities do not vary significantly, whereas we find strong variability in the closure phases, suggesting temporal variations in the asymmetric brightness distribution associated to the disk. Our observations are best fitted by a model of a crescent-like asymmetric dust feature located at ~1 au and accounting for ~70 % of the near-infrared (NIR) emission. The feature has an almost constant magnitude and orbits the central star with a possible sub-Keplerian period of ~12 months, although a 9 month period is another, albeit less probable, solution. The radiative transfer models show that the emission originates from a small amount of carbon-rich (25%) silicates, or quantum-heated particles located in a low-density region. Among different possible scenarios, we favor hydrodynamical instabilities in the inner disk that can create a large vortex. The high spectral resolution differential phases in the Brγ line show that the hot-gas compact component is offset from the star and in some cases is located between the star and the crescent feature. The scale of the emission does not favor magnetospheric accretion as a driving mechanism. The scenario of an asymmetric disk wind or a massive accreting substellar or planetary companion is discussed. Conclusions. With this unique observational data set for HD 98922, we reveal morphological variability in the innermost 2 au of its disk region. This property is possibly common to many other protoplanetary disks, but is not commonly observed due to a lack of high-cadence observation. It is therefore important to pursue this approach with other sources for which an extended dataset with PIONIER, GRAVITY, and possibly MATISSE is available.