Low ionization metal absorption due to OI has been identified as an important probe of the physical state of the inter-/circumgalactic medium at the tail-end of reionization. We use here high-resolution hydrodynamic simulations to interpret the incidence rate of OI absorbers at z~6 as observed by Becker et al. (2011). We infer weak OI absorbers (EW > 0.1 A) to have typical HI column densities in the range of sub-DLAs, densities of 80 times the mean baryonic density and metallicities of about 1/500 th solar. This is similar to the metallicity inferred at similar overdensities at z~3, suggesting that the metal enrichment of the circumgalactic medium around low-mass galaxies has already progressed considerably by z~6. The apparently rapid evolution of the incidence rates for OI absorption over the redshift range 5<z<6 mirrors that of self-shielded Lyman-Limit systems at lower redshift and is mainly due to the rapid decrease of the meta-galactic photo-ionization rate at z>5. We predict the incidence rate of OI absorbers to continue to rise rapidly with increasing redshift as the IGM becomes more neutral. If the distribution of metals extends to lower density regions, OI absorbers will allow the metal enrichment of the increasingly neutral filamentary structures of the cosmic web to be probed.