We report an experimental demonstration of single-photon switching in laser-cooled $^{87}$Rb atoms. A resonant probe pulse with an energy per unit area of one photon per $lambda^2/2pi$ propagates through the optically thick atoms. Its energy transmittance is greater than 63% or loss is less than $e^{-1}$ due to the effect of electromagnetically induced transparency. In the presence of a switching pulse with an energy per unit area of 1.4 photons per $lambda^2/2pi$, the energy transmittance of the same probe pulse becomes less than 37% or $e^{-1}$. This substantial reduction of the probe transmittance caused by single switching photons has potential applications in single-photon-level nonlinear optics and the manipulation of quantum information.