Abstract River deltas are important landforms because they build coasts. Primary channels divide deltaic land into islands, which must accrete sediment fast enough for deltas to keep pace with sea level rise. Field observations are critical for determining the physical mechanisms that transport sediment between primary channels and islands, but are lacking. We conducted a field study in the Wax Lake Delta, Louisiana, part of the Mississippi River Delta complex, to investigate sediment transport in a river‐dominated delta. Water surface elevation and sediment concentration time series reveal that taller levees sometimes blocked water and sediment from entering the island. Falling tide increased bed shear stress, entrainment, and sediment concentration in primary channels because muddy suspended sediment was largely flocculated and behaved like bed‐material load. Hydraulic modeling supplements the field data and reveals that a dynamic interplay of flow depth, velocity, and lateral water surface slope into the island determined the water discharge into the island wetland, which was diminished at higher depths when the hydraulic gradient became too shallow. Tides modulated primary channel sediment concentration, but river discharge primarily controlled sediment flux into the island. Island flows were sufficiently slow and shallow to facilitate mud settling in the island due in part to vegetation‐induced roughness, which is poorly constrained in existing hydrodynamic models. Ultimately, mud was supplied to the island by these transport mechanisms and readily accreted owing to its enhanced floc settling velocity. Muddy island top deposits highlight the importance of mud, rather than sand, for building islands.