In this work, we present a method to estimate the mass distribution of a rigid object through robotic interactions and tactile feedback. This is a challenging problem because of the complexity of physical dynamics modeling and the action dependencies across the model parameters. We propose a  sequential estimation strategy combined with a set of robot action selection rules based on the analytical formulation of a discrete-time dynamics model. To evaluate the performance of our approach, we also manufactured re-configurable block objects that allow us to modify the object mass distribution while having access to the ground truth values. We compare our approach against multiple baselines and show that our approach can estimate the mass distribution with around 10% error, while the baselines have errors ranging from 18% to 68%.