Modular multilevel converters (MMC) are increasingly gaining its importance in HVDC, drive applications due to several attributes such as modularity, scalability, low device stress, excellent output voltage waveform. For MMC operations, it is important to accurately measure the voltages across the individual capacitors of submodules (SMs). These voltage sensors, while upgrading for high voltage applications, may cause a few concerns in terms of cost, complexity, and data acquisition system. To avoid all these, a discrete time adaptive observer (DTAO) is proposed in this article to observe the voltages across the capacitors of the SMs and use the observed values for closed-loop operation of the MMC. The proposed observer is designed by considering the parametric uncertainty in the MMC and its convergence is proved mathematically. Moreover, the DTAO is compared with existing observation techniques for MMC SM capacitor voltages. The efficacy of the proposed observer is shown through simulation and validated using an experimental setup.