Astrophysical and cosmological measurements suggest that non-baryonic dark matter dominates the matter content of the Universe. However, its underlying nature remains elusive. Among the most promising candidates are weakly interacting massive particles (WIMPs): particles with mass and coupling strength at the electroweak scale and thermally produced in the early universe having a present relic density consistent with that observed today. WIMP self-annihilation could produce Standard Model particles, including gamma-rays, which have been long-time recognized as a prime messenger to indirectly detect dark matter signals. Line-like features expected in the gamma-ray spectra from WIMP self-annihilation provide a key signature for TeV-scale particle dark matter. The centre of the MilkyWay is predicted as the brightest source of DM annihilations. The H.E.S.S. collaboration is currently performing a survey of the inner region of the Milky Way, the Inner Galaxy Survey (IGS). We analyzed 2014-2020 observations taken with the five-telescope array to search for a DM line annihilation signal. With the current dataset of 546 hours, we found no significant excess and therefore derived strong constraints on the velocity-weighted annihilation cross-section into two gammas. Our limits significantly improve the current constraints, opening the possibility of constraining canonical thermal Dark Matter models with prominent line contribution in their annihilation spectra, as expected in the Wino and Higgsino cases.