Irradiation with Pb ions was used to study the effect of disorder on the in-plane London penetration depth, λ(T), in single crystals of Ba(Fe1−xTx)2As2 (T=Co, Ni). An increase in the irradiation dose results in a monotonic decrease in the superconducting transition temperature, Tc, without affecting much the transition width. In both Co- and Ni-doped systems we find a power-law behavior, Δλ(T)∝Tn with the exponent n systematically decreasing with the increase in disorder. This observation, at qualitative odds with the response of s- and d-wave superconductors, finds natural explanation in a nodeless s± state with pairbreaking (interband) impurity scattering. We are able to describe the effect quantitatively assuming the pairbreaking strength intermediate between Born and unitary limits.