We present deep infrared (Ks-band) imaging polarimetry and radio (1.4- and 4.8-GHz) polarimetry of the enigmatic transient Swift J164449.3+573451. This source appears to be a short-lived jet phenomenon in a galaxy at redshift z= 0.354, activated by a sudden mass accretion on to the central massive black hole, possibly caused by the tidal disruption of a star. We aim to find evidence for this scenario through linear polarimetry, as linear polarization is a sensitive probe of jet physics, source geometry and the various mechanisms giving rise to the observed radiation. We find a formal Ks-band polarization measurement of Plin= 7.4 ± 3.5 per cent (including systematic errors). Our radio observations show continuing brightening of the source, which allows sensitive searches for linear polarization as a function of time. We find no evidence of linear polarization at radio wavelengths of 1.4 and 4.8 GHz at any epoch, with the most sensitive 3σ limits as deep as 2.1 per cent. These upper limits are in agreement with expectations from scenarios in which the radio emission is produced by the interaction of a relativistic jet with a dense circumsource medium. We further demonstrate how polarization properties can be used to derive properties of the jet in Swift J164449.3+573451, exploiting the similarities between this source and the afterglows of gamma-ray bursts.