This study introduces a short-time Fourier transform-based method for reconstructing signals encoded using modulo analog-to-digital converters with 1-bit folding information. In contrast to existing Fourier-based reconstruction approaches that require complete access to the entire observation, the proposed technique performs reconstruction over short, overlapping segments, enabling significantly lower latency while preserving the recovery accuracy. We also address the spectral leakage introduced by the windowing operation by selecting window parameters that balance the leakage suppression and the computational complexity of the algorithm. In addition, we establish conditions under which the correct unfolding of the modulo samples is guaranteed, leading to a reconstruction error determined solely by the quantization noise at the output. The numerical results demonstrate that the proposed method enables modulo analog-to-digital converters to surpass the mean squared error performance of conventional analog-to-digital converters. Furthermore, the proposed recovery method offers improved reconstruction performance compared with higher-order difference-based recovery, particularly in low-resolution and low-sampling rate regimes.