Submarine permafrost degradation has been invoked as a cause for recent observations of methane emissions from the seabed to the water column and atmosphere of the East Siberian shelf. Sediment drilled 52 m down from the sea ice in Buor Khaya Bay, central Laptev Sea revealed unfrozen sediment overlying ice‐bonded permafrost. Methane concentrations in the overlying unfrozen sediment were low (mean 20 µM) but higher in the underlying ice‐bonded submarine permafrost (mean 380 µM). In contrast, sulfate concentrations were substantially higher in the unfrozen sediment (mean 2.5 mM) than in the underlying submarine permafrost (mean 0.1 mM). Using deduced permafrost degradation rates, we calculate potential mean methane efflux from degrading permafrost of 120 mg m−2 yr−1 at this site. However, a drop of methane concentrations from 190 µM to 19 µM and a concomitant increase of methane δ13C from −63‰ to −35‰ directly above the ice‐bonded permafrost suggest that methane is effectively oxidized within the overlying unfrozen sediment before it reaches the water column. High rates of methane ebullition into the water column observed elsewhere are thus unlikely to have ice‐bonded permafrost as their source.