A greedy algorithm is proposed for sparse-sensor selection in reduced-order sensing that contains correlated noise in measurement. The sensor selection is carried out by maximizing the determinant of the Fisher information matrix in a Bayesian estimation operator.The Bayesian estimation with a covariance matrix of the measurement noise and a prior probability distribution of estimating parameters, which are given by the modal decomposition of high dimensional data, robustly works even in the presence of the correlated noise. After computational efficiency of the algorithm is improved by a low-rank approximation of the noise covariance matrix, the proposed algorithms are applied to various problems. The proposed method yields more accurate reconstruction than the previously presented method with the determinant-based greedy algorithm, with reasonable increase in computational time.