The nuclear modification factor, $R_{\rm AA}$, of the prompt charmed mesons ${\rm D^0}$, ${\rm D^+}$ and ${\rm D^{*+}}$, and their antiparticles, was measured with the ALICE detector in Pb-Pb collisions at a centre-of-mass energy $\sqrt{s_{\rm NN}} = 2.76$ TeV in two transverse momentum intervals, $5<p_{\rm T}<8$ GeV/$c$ and $8<p_{\rm T}<16$ GeV/$c$, and in six collision centrality classes. The $R_{\rm AA}$ shows a maximum suppression of a factor of 5-6 in the 10% most central collisions. The suppression and its centrality dependence are compatible within uncertainties with those of charged pions. A comparison with the $R_{\rm AA}$ of non-prompt ${\rm J}/\psi$ from B meson decays, measured by the CMS Collaboration, hints at a larger suppression of D mesons in the most central collisions.
${\rm D^+}$ meson $R_{\rm AA}$ in $5 < p_{\rm T} < 8$ GeV/c.
${\rm D^+}$ meson $R_{\rm AA}$ in $8 < p_{\rm T} < 16$ GeV/c.
${\rm D^{*+}}$ meson $R_{\rm AA}$ in $5 < p_{\rm T} < 8$ GeV/c.