Slip detection is of fundamental importance for the safety and efficiency of rovers driving on the surface of extraterrestrial bodies. Current planetary rover slip detection systems rely on visual perception on the assumption that sufficient visual features can be acquired in the environment. However, visual-based methods are prone to suffer in perceptually degraded planetary environments with dominant low terrain features such as regolith, glacial terrain, salt-evaporites, and poor lighting conditions such as dark caves and permanently shadowed regions. Relying only on visual sensors for slip detection also requires additional computational power and reduces the rover traversal rate. This paper answers the question of how to detect wheel slippage of a planetary rover without depending on visual perception. In this respect, we propose a slip detection system that obtains its information from a proprioceptive localization framework that is capable of providing reliable, continuous, and computationally efficient state estimation over hundreds of meters. This is accomplished by using zero velocity update, zero angular rate update, and non-holonomic constraints as pseudo-measurement updates on an inertial navigation system framework. The proposed method is evaluated on actual hardware and field-tested in a planetary-analog environment. The method achieves greater than 92% slip detection accuracy for distances around 150 m using only an IMU and wheel encoders.