We report on near-infrared J- and H-band linear polarimetric photometry of eight ultracool dwarfs (two late-M, five L0-L7.5, and one T2.5) with known evidence for photometric variability due to dust clouds, anomalous red infrared colors, or low-gravity atmospheres. The polarimetric data were acquired with the LIRIS instrument on the William Herschel Telescope. We also provide mid-infrared photometry in the interval 3.4-24 μm for some targets obtained with Spitzer and WISE, which has allowed us to confirm the peculiar red colors of five sources in the sample. We can impose modest upper limits of 0.9% and 1.8% on the linear polarization degree for seven targets with a confidence of 99%. Only one source, 2MASS J02411151-0326587 (L0), appears to be strongly polarized (P ~ 3%) in the J band with a significance level of P/σ P ~ 10. The likely origin of its linearly polarized light and rather red infrared colors may reside in a surrounding disk with an asymmetric distribution of grains. Given its proximity (66 ± 8 pc), this object becomes an excellent target for the direct detection of the disk.