Extremely long and thin nanocomposite fibers are prepared by oxidative polymerization of pyrrole (or aniline) around the surfaces of copper hydroxide nanostrands. The individual nanostrands of 2.5 nm are uniformly coated with a polypyrrole layer of 3 to 4 nm, resulting in hybrid core/shell fibers of about 10 nm in diameter and a few micrometers in length, as confirmed by high‐resolution electron microscopy. The as‐prepared nanocomposite fibers are dispersive in water and can be converted into thin free‐standing films by simply filtering a small volume of the aqueous solution using a polycarbonate membrane filter. The films covering the submicrometer pores of the membrane filter have a thickness of a few tens of nanometers, and provide a mechanically stable nanofiber network with abundant pores of a few nanometers. The network is stable in acidic and basic media, and can be used for protein separation under pressures of at least 90 kPa. The permeation rates of cytochrome c, myoglobin, and ferritin were examined by changing the pH around their isoelectric points. It is seen that the nanofibrous free‐standing films on the polycarbonate membrane filter show clear size selectivity for the proteins, retaining extremely high filtration rates for water. We demonstrate herein durable mesoporous separation membranes made of organic–inorganic nanocomposite fibers and their outstanding performance.