Let X be a compact quotient of the product of the real Heisenberg group H 4m+1 of dimension 4m + 1 and the three-dimensional real Euclidean space R 3 . A left-invariant hypercomplex structure on H 4m+1 × R 3 descends onto the compact quotient X. The space X is a hyperholomorphic fibration of 4-tori over a 4m-torus. We calculate the parameter space and obstructions to deformations of this hypercomplex structure on X. Using our calculations, we show that all small deformations generate invariant hypercomplex structures on X but not all of them arise from deformations of the lattice. This is in contrast to the deformations on the 4m-torus.