We present Spitzer Space Telescope photometry of 18 Sloan Digital Sky Survey (SDSS) quasars at 2.7 <= z <= 5.9 which have weak or undetectable high-ionization emission lines in their rest-frame ultraviolet (UV) spectra (hereafter weak-lined quasars, or WLQs). The Spitzer data are combined with SDSS spectra and ground-based, near-infrared (IR) photometry of these sources to produce a large inventory of spectral energy distributions (SEDs) of WLQs across the rest-frame ~0.1-5 mum spectral band. The SEDs of our sources are inconsistent with those of BL Lacertae objects which are dominated by synchrotron emission due to a jet aligned close to our line-of-sight, but are consistent with the SED of ordinary quasars with similar luminosities and redshifts that exhibit a near-to-mid-IR bump, characteristic of hot dust emission. This indicates that broad emission lines in WLQs are intrinsically weak, rather than suffering continuum dilution from a jet, and that such sources cannot be selected efficiently from traditional photometric surveys.