The effect of metal inert gas welding on the microstructure, abnormal grain growth and the pseudoelastic properties of industrially processed Fe–Mn–Al–Ni shape memory alloy sheets were studied. Square-butt welds were manufactured using similar filler material. The influence of alternating mean arc linear energy on the microstructure of the individual zones is shown. A correlation between the process parameters, the associated heat input, the grain morphology and the α/γ-ratio could be deduced. As the mean arc linear energy increases, the α/γ-ratio in the fusion zone and the heat-affected zone increases. To evaluate the influence of the welding process on abnormal grain growth, a post-weld cyclic heat-treatment was carried out. Although no loss of major alloying elements in the fusion zone was observed after welding, metal inert gas welding has a significant effect on grain growth upon cyclic heat treatment. While abnormal grain growth occurred in the base material, a polycrystalline microstructure characterized by significantly smaller grain sizes was visible in the former fusion zone. Incremental strain tests revealed severe plastic deformation near the grain boundaries in the former fusion zone. However, the grain boundaries of the bamboo-like grown grains in the base material turned out to be more critical for structural failure.