A low-complexity signal detection approach based on the Kaczmarz algorithm (KA) is proposed to iteratively realize minimum mean square error (MMSE) detection for uplink massive multiple-input multiple-output (MIMO) systems. While KA is used for straightforward matrix inversion, the MMSE detection requires the computation of the Gram matrix with high complexity. In order to avoid the Gram matrix computation, an equivalent augmented matrix is applied to KA-based MMSE detection. Moreover, promising initial estimation and an approximate method to compute soft-output information are utilized to further accelerate the convergence rate and reduce the complexity. Simulation results demonstrate that the proposed approach outperforms the recently proposed Neumann series, conjugate gradient, and Gauss-Seidel methods in complexity and error-rate performance. Meanwhile, the FPGA implementation results confirm that our proposed method can efficiently compute the approximate inverse with low complexity.