The proposed Daksha mission comprises of a pair of highly sensitive space telescopes for detecting and characterizing high-energy transients, such as electromagnetic counterparts of gravitational wave events and gamma-ray bursts (GRBs). Along with spectral and timing analysis, Daksha can also undertake polarization studies of these transients, providing data crucial for understanding the source geometry and physical processes governing high-energy emission. Each Daksha satellite will have 340 pixelated cadmium zinc telluride (CZT) detectors arranged in a quasi-hemispherical configuration without any field-of-view collimation (open detectors). These CZT detectors are good polarimeters in the energy range 100 to 400 keV, and their ability to measure polarization has been successfully demonstrated by the cadmium zinc telluride imager onboard AstroSat. Here, we demonstrate the hard x-ray polarization measurement capabilities of Daksha and estimate the polarization measurement sensitivity (in terms of the minimum detectable polarization: MDP) using extensive simulations. We find that Daksha will have MDP of 30% for a fluence threshold of 10 ^{− 4} erg cm ^{− 2} (in 10 to 1000 keV). We estimate that with this sensitivity, if GRBs are highly polarized, Daksha can measure the polarization of about five GRBs per year.