  We study the six-dimensional $\cal{N}=(1,0)$ supersymmetric hypermultiplet
model with arbitrary self-coupling. The model is considered in the external
classical gauge superfield background. Using the harmonic superspace
formulation we study the one-loop effective action of the model. We calculate
the one-loop divergences in the theory as a gauge-invariant function of the
external gauge multiplet. We demonstrate that the one-loop divergences in the
theory do not vanish even in the case of on-shell hypermultiplet background. We
briefly discuss an application of the developed technique to the hypermultiplet
model in four dimensions.
