We obtained linear polarization photometry (J-band) and low-resolution spectroscopy (ZJ-bands) of TRAPPIST-1, which is a planetary system formed by an M8-type low-mass star and seven temperate, Earth-sized planets. The photopolarimetric monitoring campaign covered 6.5 h of continuous observations including one full transit of planet TRAPPIST-1d and partial transits of TRAPPIST-1b and e. The spectrophotometric data and the photometric light curve obtained over epochs with no planetary transits indicate that the low-mass star has very low level of linear polarization compatible with a null value. However, the `in transit' observations reveal an enhanced linear polarization signal with peak values of p^* = 0.1 {{ per cent}} with a confidence level of 3σ, particularly for the full transit of TRAPPIST-1d, thus confirming that the atmosphere of the M8-type star is very likely dusty. Additional observations probing different atmospheric states of TRAPPIST-1 are needed to confirm our findings, as the polarimetric signals involved are low. If confirmed, polarization observations of transiting planetary systems with central ultracool dwarfs can become a powerful tool for the characterization of the atmospheres of the host dwarfs and the validation of transiting planet candidates that cannot be corroborated by any other method.