  The Higgs invisible decay width may soon become a powerful tool to probe
extensions of the Standard Model with dark matter candidates at the Large
Hadron Collider. In this work, we calculate the next-to-leading order (NLO)
electroweak corrections to the 125 GeV Higgs decay width into two dark matter
particles. The model is the next-to-minimal 2-Higgs-doublet model (N2HDM) in
the dark doublet phase, that is, only one doublet and the singlet acquire
vacuum expectation values. We show that the present measurement of the Higgs
invisible branching ratio, BR$(H \to$ invisible $< 0.11$), does not lead to
constraints on the parameter space of the model at leading order. This is due
to the very precise measurements of the Higgs couplings but could change in the
near future. Furthermore, if NLO corrections are required not to be
unphysically large, no limits on the parameter space can be extracted from the
NLO results.
