A density-dependent gauge field may induce density-induced geometric frustration, leading to a non-trivial interplay between density modulation and frustration, which we illustrate for the particular case of ultra-cold bosons in zig-zag optical lattices with a density-dependent hopping amplitude. We show that the density-induced frustration leads to a rich landscape of quantum phases, including Mott insulator, bond-order insulator, two-component superfluids, chiral superfluids, and partially paired superfluids. We show as well that the density-dependent hopping results in an effective repulsive or attractive interaction, and that for the latter case the vacuum may be destabilized leading to a strong compressibility. Finally, we discuss the characteristic momentum distribution of the predicted phases, which can be used to detect the phases in time-of-flight measurements.