We present the results of a survey of a small sample (14) of low-mass protostars (L_IR < 10³ L) for 6.7 GHz methanol maser emission performed using the ATNF Parkes radio telescope. No new masers were discovered. We find that the lower luminosity limit for maser emission is near 10³ L by comparison of the sources in our sample with previously detected methanol maser sources. We examine the IRAS properties of our sample and compare them with sources previously observed for methanol maser emission, almost all of which satisfy the Wood & Churchwell criterion for selecting candidate UC H II regions. We find that about half of our sample satisfy this criterion, and in addition, almost all of this subgroup have integrated fluxes between 25 and 60 μm that are similar to sources with detectable methanol maser emission. By identifying a number of low-mass protostars in this work and from the literature that satisfy the Wood & Churchwell criterion for candidate UC H II regions, we show conclusively for the first time that the fainter flux end of their sample is contaminated by lower mass nonionizing sources, confirming the suggestion by van der Walt and Ramesh & Sridharan.