Within QCD sum rules at finite baryon density we show the crucial role of four-quark condensates, such as 〈(q̄γμλ^aq)²〉n, for the in-medium modification of the ω meson spectral function. In particular, such a global property as the sign of the inmedium ω meson mass shift is found to be governed by a parameter which describes the strength of the density dependence of the four-quark condensate beyond mean-field approximation. To study self-consistently the broadening of the ω meson resonance we employ a hadron spectral function based on the ω meson propagator delivered by an effective chiral Lagrangian. Measurements of the ω meson spectral change in heavy-ion collisions with the HADES detector can reveal the yet unknown density dependence of the four-quark condensate.