The present invention relates to an implantable device for the selective removal of molecules from tissues or fluids so as to allow the selective removal of a particular molecule of interest (target molecule) from any type of fluid solution or tissue, including biological tissues or fluids. The device operates by means of the complementary action of specific-binding molecules (6) (antibodies) directed against the target molecule (4) inside the device, and a nanoperforated membrane (8) having pores larger than the target molecule (4) but smaller than the antibodies, such that the fluid can be removed through a second catheter (9) with a lower concentration of target molecules (4).