  Recently, the CDF collaboration has reported a new precision measurement of
the $W$-boson mass, $M_W$, showing a large deviation from the value predicted
by the Standard Model (SM). In this paper, we analyse possible new physics
contributions to $M_W$ from extended Higgs sectors. We focus on the
Two-Higgs-Doublet Model (2HDM) as a concrete example. Employing predictions for
the electroweak precision observables in the 2HDM at the two-loop level and
taking into account further theoretical and experimental constraints, we
identify parameter regions of the 2HDM in which the prediction for $M_W$ is
close to the new CDF value. We assess the compatibility of these regions with
precision measurements of the effective weak mixing angle and the total width
of the $Z$ boson.
