The fraction of AGN luminosity obscured by dust and re-emitted in the mid-IR is critical for understanding AGN evolution, unification, and parsec-scale AGN physics. For unobscured (Type-1) AGN, where we have a direct view of the accretion disk, the dust covering factor can be measured by computing the ratio of re-processed mid-IR emission to intrinsic nuclear bolometric luminosity. We use this technique to estimate the obscured AGN fraction as a function of luminosity and redshift for 513 Type-1 AGN from the XMM-COSMOS survey. The re-processed and intrinsic luminosities are computed by fitting the 18-band COSMOS photometry with a custom SED-fitting code, which jointly models emission from: hot-dust in the AGN torus, the accretion disk, and the host-galaxy. We find a relatively shallow decrease of the luminosity ratio as a function of Lbol, which we interpret as a corresponding decrease in the obscured fraction. In the context of the receding torus model, where dust sublimation reduces the covering factor of more luminous AGN, our measurements require a torus height which increases with luminosity as h ~ Lbol^{0.3-0.4}. Our obscured fraction-luminosity relation agrees with determinations from SDSS censuses of Type-1 and Type-2 quasars, and favors a torus optically thin to mid-IR radiation. We find a much weaker dependence of obscured fraction on 2-10 keV luminosity than previous determinations from X-ray surveys, and argue that X-ray surveys miss a significant population of highly obscured Compton-thick AGN. Our analysis shows no clear evidence for evolution of obscured fraction with redshift.