The J-PARC KOTO experiment aims to explore new physics beyond the Standard Model through the $K_L$ → $π^0v\bar{v}$ decay. Here we installed a new photon-veto detector, named the Inner Barrel (IB), to improve the detection efficiency and the timing resolution for photons in the region transverse to the neutral beam. The IB is a 2.8-m-long cylindrical detector with a 1.5 m inner diameter. The IB is a lead-scintillator sampling shower counter with a 5-radiation-length thickness and with a low mass support structure, and fits inside the 14-radiation-length-thick cylindrical detector. Scintillating light is read out from both ends via wavelength shifting fibers with a short decay time. The design, construction and performance of the IB are presented in this paper.