It is often required to estimate the minimum sizes of 2D finite-impulse response (FIR) filters with magnitude constraints in filter design tasks. Complete exploring of estimation formulas is difficult because of infinite number of possible frequency response (FR) geometries in 2D filters. Instead, this letter presents an online procedure that rapidly estimates the minimum size for given FR specifications. The procedure is based on two interesting experimental observations on the logarithmic mean square normalized magnitude error of least-square filters. Applications to frequency-selective filters with different FR specifications demonstrate the effectiveness and efficiency of the procedure.