A defining characteristic of fractured rocks is their very high level of seismic attenuation, which so far has been assumed to be mainly due to wave-induced fluid flow (WIFF) between the fractures and the pore space of the embedding matrix. Using oscillatory compressibility simulations based on the quasi-static poroelastic equations, we show that another important, and as of yet undocumented, manifestation of WIFF is at play in the presence of fracture connectivity. This additional energy loss is predominantly due to fluid flow within the connected fractures and is sensitive to their lengths, permeabilities, and intersection angles. Correspondingly, it contains key information on the governing hydraulic properties of fractured rock masses and hence should be accounted for whenever realistic seismic models of such media are needed.