The Giant Metrewave Radio Telescope (GMRT) reionization effort aims to map out the large-scale structure of the Universe during the epoch of reionization (EoR). Removal of polarized Galactic emission is a difficult part of any 21 cm EoR programme, and we present new upper limits to diffuse polarized foregrounds at 150 MHz. We find no high-significance evidence of polarized emission in our observed field at mid-galactic latitude (J2000 08h26m+26). We find an upper limit on the two-dimensional angular power spectrum of diffuse polarized foregrounds of (l2Cl/2π)1/2 < 3 K in frequency bins of width δν= 1 MHz at 300 < l < 1000. The three-dimensional power spectrum of polarized emission, which is most directly relevant to EoR observations, is [k3PP(k)/2π2]1/2 < 2 K at k⊥ > 0.03 h Mpc−1, k < 0.1 h Mpc−1. This can be compared to the expected EoR signal in total intensity of [k3P(k)/2π2]1/2∼ 10 mK. We find that polarized structure is substantially weaker than suggested by extrapolation from higher frequency observations, so the new low upper limits reported here reduce the anticipated impact of these foregrounds on EoR experiments. We discuss the Faraday beam and depth depolarization models and compare predictions of these models to our data. We report on a new technique for polarization calibration using pulsars, as well as a new technique to remove broad-band radio frequency interference. Our data indicate that, on the edges of the main beam at the GMRT, polarization squint creates ∼3 per cent leakage of unpolarized power into polarized maps at zero rotation measure. Ionospheric rotation was largely stable during these solar minimum nighttime observations.