We present equivalent width measurements and limits of six diffuse interstellar bands (DIBs, λ 4428, λ 5705, λ 5780, λ 5797, λ 6284, and λ 6613) in seven damped Lyα absorbers (DLAs) over the redshift range 0.091 ≤ z ≤ 0.524, sampling 20.3 ≤ log N(Hi) ≤ 21.7. Based upon the Galactic DIB–N(H i) relation, the λ 6284 DIB equivalent width upper limits in four of the seven DLAs are a factor of 4–10 times below the λ 6284 DIB equivalent widths observed in the Galaxy, but are not inconsistent with those present in the Magellanic Clouds. Assuming the Galactic DIB–E(B − V) relation, we determine reddening upper limits for the DLAs in our sample. Based upon the E(B − V) limits, the gas-to-dust ratios, N(H i)/E(B − V), of the four aforementioned DLAs are at least ~5 times higher than that of the Galactic ISM and are more consistent with the Large Magellanic Cloud. The ratios of two other DLAs are at least a factor of a few times higher. The best constraints on reddening derive from the upper limits for the λ 5780 and λ 6284 DIBs, which yield E(B − V) ≤ 0.08 mag for four of the seven DLAs and are more consistent with the Magellanic Clouds rather than the Galaxy. Our results suggest that, in DLAs, quantities related to dust, such as reddening and metallicity, appear to have a greater impact on DIB strengths than does H i gas abundance. The molecules responsible for the DIBs in DLA selected sightlines are underabundant relative to sightlines in the Galaxy of similarly high N(H i). Using DIBs to study the ISM of DLAs provide evidence that at least some population of DLAs are more Magellanic-like than Galactic-like.