In off-axis digital holography, the Fourier transform-based algorithm is commonly used for signal processing. Here, we derive the theoretical phase sensitivity of this algorithm, which can be calculated from a single 2D hologram. This algorithm sensitivity represents the best achievable sensitivity of a system using this algorithm. Our derivation treats the signal in its most general form, considering non-uniform illumination and the effect of sideband filtering. As a result, phase sensitivity varies spatially, determined by local signal-to-noise ratio. Sensitivity expressions for both shot noise and uniform noise models are given. These results are validated with simulations and experiments. Significantly, this theoretical sensitivity can serve as a baseline metric for assessing performance of a phase-imaging system, such as experimental sensitivity and hardware stability, which are critical for high-sensitivity quantitative phase imaging. In addition, the results are equally applicable to other interferometric techniques with similar interferogram patterns and signal processing algorithms.