In this paper, we introduce a 3-dimensional, distributed, iterative, and 'silent' localization protocol for Mobile Underwater Sensor Networks (MUSNs) named as Mobility Assisted Localization Scheme (MobiL). The existing solutions addressing the localization problem in underwater sensor networks (UWSNs) either consider the sensor nodes to be stationary or require powerful nodes, which can directly communicate with the surface sinks. Such assumptions are not applicable in MUSNs, where sensor nodes are affected by passive node mobility and the acoustic communication channel is severely impaired by high propagation loss. On the other hand, MobiL requires only three anchor nodes capable of providing the initial location beacon and all other nodes are ordinary sensor nodes. We exploit the spatially correlated mobility pattern of UWSNs and apply it to localize the sensor nodes. Also, we employ the 'silent' listening of beacon messages, which empowers MobiL to be energy-efficient. Simulations in NS-3 show that the proposed scheme successfully localizes nearly 90% of the total sensor nodes with localization error in the order of 25-30% of the error threshold in highly mobile UWSNs.