Supernova (SN) explosions interacting with dense circumstellar medium are considered to be very promising sites for efficient cosmic-ray (CR) acceleration and subsequent emission of neutral- pion-decay gamma rays. These environments share similarities with already detected gamma-ray novae, but with much greater available energy content, so it is important to characterize their emission in the very-high-energy range. We present the results of H.E.S.S. observations of one such candidate source – SN 2024ggi, located in NGC 3621 at a distance of 7.24 Mpc. A total of 30 hours of data, gathered throughout a month of post-explosion observations, provide flux upper limits that are used to constrain source parameters, offering meaningful insights for theoretical predictions. We exclude bright gamma-ray emission in the first day after explosion, and later upper limits are consistent with wind densities derived from optical observations.