Floods cause more damage in Russia than any other natural disaster, and future climate model projections suggest that the frequency and magnitude of extreme hydrological events will increase in Russia with climate change. Here we analyze daily discharge records from a new data set of 139 Russian gauges in the Eurasian Arctic drainage basin with watershed areas from 16.1 to 50,000 km2 for signs of change in maximum river discharge. Several hypotheses about changes in maximum daily discharge and their linking with trends in precipitation over the cold season were tested. For the magnitude of maximum daily discharge we found relatively equal numbers of significant positive and negative trends across the Russian Arctic drainage basin, which draws into question the hypothesis of an increasing risk of extreme floods. We observed a significant shift to earlier spring discharge, which is consistent with documented changes in snowmelt and freeze‐thaw dates. Spatial analysis of changes in maximum discharge and cold season precipitation revealed consistency across most of the domain, the exception being the Lena basin. Trends in maximum discharge of the small‐ to medium‐sized rivers were generally consistent with aggregated signals found for the downstream gauges of the six largest Russian rivers. Although we observe regional changes in maximum discharge across the Russian Arctic drainage basin, no evidence of widespread trends in extreme discharge can be assumed from our analysis.