We investigate extension of a vertical crack filled by water and methane gas induced by dissociation of methane hydrate in low‐permeability muddy sediment. We model the sediment as an impermeable elastic medium and consider a thin sheet configuration of hydrate that initially occupies a vertical fracture. The crack development and the amount of dissociated hydrate are determined using sediment elasticity, fracture mechanics, kinetics of hydrate dissociation, and the equation of state for methane gas. Young's modulus and fracture toughness of the sediment greatly affect the mass of hydrate required for crack extension; lower Young's modulus and higher fracture toughness require greater hydrate mass to induce unstable, buoyancy‐driven crack propagation. Our numerical results suggest that propagation of gas/water‐filled cracks occurs quickly in a matter of seconds and may be an important mechanism for methane transport in low‐permeability sediments when hydrate‐filled fractures are under conditions of gas hydrate dissociation.