Modular Multilevel Converters(MMCs) are considered to be state-of-the-art power converters for high voltage applications. MMCs typically consist of a stack of capacitorswitch assemblies (known as sub-modules), and requires voltage balancing control of multiple floating capacitors. To make these control decisions accurate, it is necessary to have precise knowledge about voltages across each of these capacitors at every instant. But, measurement of exact capacitor voltages in the MMC becomes difficult as the number of submodules increases. We propose a technique for tracking capacitor voltages in the MMC by using only load voltage and current measurements. Initially, a few voltage and current measurements from the load-end were used to estimate the load parameters. As a part of the prediction scheme, we used a plant model for an MMC, which takes the sum of voltages across all the capacitances in an arm, as a lumped parameter. We simulated this plant model with our estimated load parameters in order to predict the voltages across each of the capacitances individually, over a prediction window. Experiments were performed, with varying prediction window(upto 4 cycles), varying loading conditions, and with different starting points. The predicted capacitance voltages were compared with actual capacitance voltages observed from the circuit simulator. Overall, our predictor presented an RMS error of less than 5% across all the various tests. It was also able to predict the relative ranking of the capacitance voltages correctly in 99.79% of all the test cases. Since, the working principle of the voltage balancing controller depends directly on the relative ranking of voltages across each of the individual capacitances, our predictor will be able to assist the controller take faster, and accurate control decisions with significantly less number of measurements.