The minimum-energy paths for the diffusion of an interstitial O atom in silicon and germanium are studied through the nudged-elastic-band method and hybrid functional calculations. The reconsideration of the diffusion of O in silicon primarily serves the purpose of validating the procedure for studying the O diffusion in germanium. Our calculations show that the minimum energy path goes through an asymmetric transition state in both silicon and germanium. The stability of these transition states is found to be enhanced by the generation of unpaired electrons in the highest occupied single-particle states. Calculated energy barriers are 2.54 and 2.14 eV for Si and Ge, in very good agreement with corresponding experimental values of 2.53 and 2.08 eV, respectively.