  We study the post-inflationary dynamics of the Standard Model (SM) Higgs
field in the presence of a non-minimal coupling $\xi|\Phi|^2R$ to gravity, both
with and without the electroweak gauge fields coupled to the Higgs. We assume a
minimal scenario in which inflation and reheating are caused by chaotic
inflation with a quadratic potential, and no additional new physics is relevant
below the Planck scale. By using classical real-time lattice simulations with a
renormalisation group improved effective Higgs potential and by demanding the
stability of the Higgs vacuum after inflation, we obtain upper bounds for
$\xi$, taking into account the experimental uncertainty of the top-Yukawa
coupling. We compare the bounds in the absence and presence of the electroweak
gauge bosons, and conclude that the addition of gauge interactions has a rather
minimal impact. In the unstable cases, we parametrize the time when such
instability develops. For a top-quark mass $m_t \approx173.3 {\rm GeV}$, the
Higgs vacuum instability is triggered for $\xi \gtrsim 4 -5$, although a
slightly lower mass of $m_t \approx 172.1 {\rm GeV}$ pushes up this limit to
$\xi \gtrsim 11 - 12$. This, together with the estimation $\xi \gtrsim 0.06$
for stability during inflation, provides tight constraints to the
Higgs-curvature coupling within the SM.
