A porous tubular support (1) for a tangential filtration membrane, in the form of a sintered monolithic ceramic porous body, manufactured by extrusion of a ceramic composition including a powdery solid inorganic phase and in which are arranged by extrusion using punches, a rectilinear channel (2a) centered on an axis of symmetry of the support and at least one circulation channel (2) for a fluid medium to be treated with a helical shape wound around the axis of symmetry, the channels having a limited wall roughness and lower than the granularity of the powdery solid inorganic phase of the ceramic composition.