The holographic entanglement entropy (HEE) of the minimal geometrical deformation (MGD) procedure and extensions (EMGD), is scrutinized within the membrane paradigm of AdS/CFT. The HEE corrections of the Schwarzschild and Reissner--Nordstrom solutions, due to a finite fluid brane tension, are then derived and discussed in the context of the MGD and the EMGD.