  Building on general formulas obtained from the approximate renormalized
effective action, the stress-energy tensor of the quantized massive spinor and
vector fields in the spacetime of the regular black hole is constructed. Such a
black hole is the solution to the coupled system of nonlinear electrodynamics
and general relativity. A detailed analytical and numerical analysis of the
stress-energy tensor in the exterior region is presented. It is shown that for
small values of the charge as well as large distances from the black hole the
leading behavior of the stress-energy tensor is similar to that in the
Reissner-Nordstr\"om geometry. Important differences appear when the inner
horizon becomes close to the event horizon. A special emphasis is put on the
extremal configuration and it is shown that the stress-energy tensor is regular
inside the event horizon of the extremal black hole.
