In this paper, we apply a block-based compressive sensing (BCS) architecture to address the reconstruction of underwater acoustic intensity fields. Although with anisotropic characteristics, underwater acoustic intensity fields can be compressed or represented in sparse transform domains. The distinct advantages of the BCS method include no need for any prior knowledge of the interested acoustic fields and no need for complete sampling coverage. Both benefits can facilitate experimentation and improve reconstruction precision. We demonstrated the recovery capability by applying this algorithm to the reconstruction of simulated acoustic fields in the Gulf of Mexico, where the bathymetry and water column showed high levels of spatial variability. Further, a field experiment was conducted at a local river, Lake Tamaha, where an autonomous underwater vehicle navigated during acoustic transmissions. Reconstruction performance comparisons were made between the BCS and interpolation methods at different measurement ratios.