We propose that the narrow 12CO and 13CO J=6-5 emission observed toward many low-mass young stellar objects is produced in molecular material in the circumstellar envelope, which is heated by the 10,000 K radiation field generated in the inner part of the accretion disk. Ultraviolet photons traveling through the biconical cavity evacuated by the bipolar outflow are scattered by dust grains present in the low-density material in the cavity. These photons are not energetic enough to photodissociate H2 and CO, but can heat the envelope surrounding the cavity. The temperature structure and the CO excitation of this photon-dominated region are computed using two-dimensional Monte Carlo methods. It is found that the material is heated up to a few hundred K close to the cavity wall, and that the observed low-velocity mid-J CO emission can be well explained by our model for a wide range in envelope density and stellar luminosity. Emergent CO spectra are compared to observations of the embedded low-mass YSO IRAS 04361+2547 (TMR-1).