To achieve fast and selective molecular filtration, membrane materials must ideally exhibit a thin porous skin and a high density of pores with a narrow size distribution. Here, we report the fabrication of nanoporous silicon nitride membranes (NSiMs) at the full wafer scale using a versatile process combining block copolymer (BCP) self-assembly and conventional photolithography/etching techniques. In our method, self-assembled BCP micelles are used as templates for creating sub-100 nm nanopores in a thin low-stress silicon nitride layer, which is then released from the underlying silicon wafer by etching. The process yields 100 nm thick free-standing NSiMs of various lateral dimensions (up to a few mm²). We show that the membranes exhibit a high pore density, while still retaining excellent mechanical strength. Permeation experiments reveal that the molecular transport rate across NSiMs is up to 16-fold faster than that of commercial polymeric membranes. Moreover, using dextran molecules of various molecular weights, we also demonstrate that size-based separation can be achieved with a very good selectivity. These new silicon nanosieves offer a relevant technological alternative to commercially available ultra- and microfiltration membranes for conducting high resolution biomolecular separations at small scales.