The invention discloses a local heat treatment annealing apparatus and method for a blast furnace/hot-blast stove casing, which belongs to the technical field of heat treatment. The local heat treatment annealing apparatus for the blast furnace/hot-blast stove casing comprises a temperature control mechanism, wherein a heating mechanism is connected with the temperature control mechanism, and theheating mechanism is closely fit to an outer wall of the casing; a temperature detection mechanism is connected with the temperature control mechanism, the temperature detection mechanism is arrangedbetween the heating mechanism and the casing, and the temperature detection mechanism is arranged in a groove formed in a weld bead of a weld seam. By adopting the local heat treatment annealing apparatus and method, a replaced casing part of the hot-blast stove can be locally subjected to heat treatment annealing so as to eliminate residual welding stress of the casing, thereby ensuring the safeand stable operation of the hot-blast stove and the long service life of the casing.