It is important to understand how and where concentrated gas hydrates form because the gas hydrate system modulates methane flow through the seafloor and into the oceans. We investigated gas hydrate formation in relation to tectonic folding at New Zealand’s southern Hikurangi subduction margin. Concentrated gas hydrates form preferentially in strata crossing the base of the hydrate stability zone at angles greater than ∼5°. Intriguingly, concentrated deposits are more common in landward-dipping strata than seaward-dipping strata. We explain this asymmetry with a conceptual model for hydrate formation in accretionary wedges. Preferential sedimentation on the landward sides of ridges leads to pronounced gas hydrate recycling in landward-dipping strata. Together with focused fluid flow beneath the hydrate system, gas hydrate recycling favors the development of interconnected gas columns that drive gas back into the hydrate stability zone to form concentrated gas hydrates. Our results advance the understanding of gas hydrate formation in accretionary wedges, which are common global tectonic settings for gas hydrate systems.