We report intense terahertz emission from lead zirconate titanate (PZT) tubular nanostructures, which have a wall thickness around 40 nm and protrude on n-type Si substrates. Such emission is totally absent in flat PZT films or bulk; hence the effect is attributed to the nanoscale geometry of the tubes. The terahertz radiation is emitted within 0.2 ps, and the spectrum exhibits a broad peak from 2 to 8 THz. This is a gap in the frequency spectrum of conventional semiconductor terahertz devices, such as ZnTe, and an order of magnitude higher frequency peak than that in the well-studied p-InAs, due to the abnormally large carrier concentration gradient in the nanostructured PZT. The inferred mechanism is optical rectification within a surface accumulation layer, rather than the Dember effect. The terahertz emission is optically pumped, but since the tubes exhibit ferroelectric switching, electrically driven emission may also be possible. EPR reveals 02 molecules adsorbed onto the nanotubes, which may play some role in the emission.