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.