Wave‐supported fluid muds (WSFM) are a type of gravity flow that can rapidly transport sediment across continental margins. They occur when wave‐induced bed stress maintains suspended‐sediment concentrations (SSC) >10 g L−1, and sediment‐induced stratification near the top of the wave boundary layer limits upward diffusion of sediment. Observations from near‐bed instrumentation are used to evaluate the conditions under which WSFMs form on the continental shelf offshore of the Waipaoa River, NZ. An event in July 2010 featured >130 h of energetic ocean conditions, and water discharge >1900 m3 s−1. A calibrated acoustic backscatter sensor at the midshelf measured near‐bed SSC >50 g L−1, with a strong lutocline occurring >15 cm above the predicted wave‐current boundary layer, resulting in ~5 cm deposition. A velocity anomaly occurred during this time, with offshore‐directed currents faster at 1 m above bed (mab) than at 3.5 mab. Using these observations, we empirically solve a simple buoyancy‐drag force balance to estimate the gravity‐driven velocity of the WSFM, which is always <0.03 m s−1. Extending the force balance across a shelf transect suggests that WSFM‐carried sediment can reach the shelf edge in 50–240 h. Spatial and temporal patterns of deposition predicted by the gradient of modeled sediment flux correlate well with seabed observations on the Waipaoa shelf reported in Walsh et al. (2014). This study highlights the importance of WSFMs for cross‐shelf sediment transport, despite relatively slow gravity‐driven velocities and the infrequency with which they occur.