Fast radio bursts (FRBs) are an emerging class of bright, highly dispersed radio pulses. Recent work by Thornton et al. (2013) has revealed a population of FRBs in the High Time Resolution Universe (HTRU) survey at high Galactic latitudes. A variety of progenitors have been proposed including cataclysmic events at cosmological distances, Galactic flare stars, and terrestrial radio frequency interference. Here we report on a search for FRBs at intermediate Galactic latitudes ($-15^{\circ}$ $< b <$ 15$^{\circ}$) in data taken as part of the HTRU survey. No FRBs were discovered in this region. Several effects such as dispersion, scattering, sky temperature and scintillation decrease the sensitivity by more than 3$\sigma$ in $\sim$20\% of survey pointings. Including all of these effects, we exclude the hypothesis that FRBs are uniformly distributed on the sky with 99\% confidence. This low probability implies that additional factors -- not accounted for by standard Galactic models -- must be included to ease the discrepancy between the detection rates at high and low Galactic latitudes. A revised rate estimate or another strong and heretofore unknown selection effect in Galactic latitude would provide closer agreement between the surveys' detection rates. The dearth of detections at low Galactic latitude disfavors a Galactic origin for these bursts.