Anaerobic oxidation of methane coupled to nitrite reduction is a recently discovered methane sink of as yet unknown global significance. The bacteria that have been identified to carry out this process, Candidatus Methylomirabilis oxyfera, oxidize methane via the known aerobic pathway involving the monooxygenase reaction. In contrast to aerobic methanotrophs, oxygen is produced intracellularly and used for the activation of methane by a phylogenetically distinct particulate methane monooxygenase (pMMO). Here we report the fractionation factors for carbon and hydrogen during methane oxidation by an enrichment culture of M. oxyfera bacteria. In two separate batch incubation experiments with different absolute biomass and methane contents, the specific methanotrophic activity was similar and the progressive isotope enrichment identical. Headspace methane was consumed up to 98% with rates showing typical first order reaction kinetics. The enrichment factors determined by Rayleigh equations were −29.2 ± 2.6‰ for δ¹³C (ε_C) and −227.6 ± 13.5‰ for δ²H (ε_H), respectively. These enrichment factors were in the upper range of values reported so far for aerobic methanotrophs. In addition, two-dimensional specific isotope analysis (Λ = ()/()) was performed and also the determined Λ value of 9.8 was within the range determined for other aerobic and anaerobic methanotrophs. The results showed that in contrast to abiotic processes biological methane oxidation exhibits a narrow range of fractionation factors for carbon and hydrogen irrespective of the underlying biochemical mechanisms. This work will therefore facilitate the correct interpretation of isotopic composition of atmospheric methane with implications for modeling of global carbon fluxes.