We present Atacama Large Millimeter/submillimeter Array ( ALMA ) Cycle 0 Band 7 observations of an extremely metal-poor dwarf starburst galaxy in the Local Universe , SBS 0335 - 052 ( 12 + log ( O/H ) \sim 7.2 ) . With these observations , dust is detected at 870 \mu m ( ALMA Band 7 ) , but 85 % of the flux in this band is due to free-free emission from the starburst . We have compiled a spectral energy distribution ( SED ) of SBS 0335 - 052 that spans almost 6 orders of magnitude in wavelength and fit it with a spherical dust shell heated by a single-age stellar population ; the best-fit model gives a dust mass of ( 3.8 \pm 0.6 ) \times 10 ^ { 4 } M _ { \odot } . We have also constructed a SED including Herschel archival data for I Zw 18 , another low-metallicity dwarf starburst ( 12 + log ( O/H ) \sim 7.17 ) , and fit it with a similar model to obtain a dust mass of ( 3.4 \pm 1.0 ) \times 10 ^ { 2 } M _ { \odot } . It appears that for such low-metallicity dwarf galaxies , the ratio of their stellar mass to their dust mass is within the range of values found for spirals and other star-forming galaxies . However , compared with their atomic gas mass , the dust mass of SBS 0335 - 052 far exceeds the prediction of a linear trend of dust-to-gas mass ratio with metallicity , while I Zw 18 falls far below . We use gas scaling relations to assess a putative missing gas component in both galaxies and find that the missing , possibly molecular , gas in SBS 0335 - 052 is a factor of 6 times higher than the value inferred from the observed H I column density ; in I Zw 18 the missing component is much smaller . Finally , we constrain the H _ { 2 } surface density conversion factor \alpha _ { CO } with our upper limit for CO J = 3 - 2 line in SBS 0335 - 052 , and find that this is consistent with a linear or even super-linear trend of increasing \alpha _ { CO } with decreasing metallicity . Ultimately , despite their similarly low metallicity , the differences in gas and dust column densities in SBS 0335 - 052 and I Zw 18 suggest that metal abundance does not uniquely define star-formation processes . At some level , self-shielding and the survival of molecules may depend just as much on gas and dust column density as on metallicity . The effects of low metallicity may at least be partially compensated for by large column densities in the interstellar medium .