The size of the membrane-bound nucleus scales with cell size in a wide range of cell types but the mechanisms determining overall nuclear size remain largely unknown. Here we investigate the role of fission yeast inner nuclear membrane proteins in determining nuclear size, and propose that the Lap2-Emerin-Man1 domain protein Lem2 acts as a barrier to membrane flow between the nucleus and other parts of the cellular membrane system. Lem2 deletion increases membrane flow into and out of the nuclear envelope in response to changes in membrane synthesis and nucleocytoplasmic transport, altering nuclear size. The endoplasmic reticulum protein Lnp1 acts as a secondary barrier to membrane flow, functionally compensating for lack of Lem2. We propose that this is part of the mechanism that maintains nuclear size proportional to cellular membrane content and thus to cell size. Similar regulatory principles may apply to other organelles in the eukaryotic subcellular membrane network.