An analysis of complex (yielding) rheological flow behavior of 0.1 wt%, 0.13 wt%, 0.15 wt% Carbopol solutions has been carried out using MRI velocimetry within the low shear rate region (10-4-10 S-1) for gravity driven flow system. For this study, flow kinematics in a pipe was performed at the steady and creeping conditions (Re <1) to get accurate dynamic yield value of Carbopol solutions. Then we show that in this range of shear rates. MRI velocimetry works well using with using the suitable image data acquisition process. Yield stresses were achieved successfully for Carbopol solutions. The less concentrated 0.1 wt% Carbopol solution was found to have the yield stress as 9.8 Pa whereas the more concentrated 0.15 wt% Carbopol solution exhibited higher yield stress value of 54.4 Pa. These are the first measurement of yield stress of Carbopol solutions by this method in the range of 10-4-10 S-1. The MRI measurements compared well with the measurements of same samples performed on conventional rheometer in the shear rate range of 10-2-10 S-1. This study provides insights into MRI velocimetry can capture the velocity profile of flows under the creeping condition.