It has long been held that electrical excitation spreads from cell-to-cell in the heart via low resistance gap junctions (GJ). However, it has also been proposed that myocytes could interact by non-GJ-mediated “ephaptic” mechanisms, facilitating propagation of action potentials in tandem with direct GJ-mediated coupling. We sought evidence that such mechanisms contribute to cardiac conduction. Using super-resolution microscopy, we demonstrate that Na_v1.5 is localized within 200 nm of the GJ plaque (a region termed the perinexus). Electron microscopy revealed close apposition of adjacent cell membranes within perinexi suggesting that perinexal sodium channels could function as an ephapse, enabling ephaptic cell-to-cell transfer of electrical excitation. Acute interstitial edema (AIE) increased intermembrane distance at the perinexus and was associated with preferential transverse conduction slowing and increased spontaneous arrhythmia incidence. Inhibiting sodium channels with 0.5 μM flecainide uniformly slowed conduction, but sodium channel inhibition during AIE slowed conduction anisotropically and increased arrhythmia incidence more than AIE alone. Sodium channel inhibition during GJ uncoupling with 25 μM carbenoxolone slowed conduction anisotropically and was also highly proarrhythmic. A computational model of discretized extracellular microdomains (including ephaptic coupling) revealed that conduction trends associated with altered perinexal width, sodium channel conductance, and GJ coupling can be predicted when sodium channel density in the intercalated disk is relatively high. We provide evidence that cardiac conduction depends on a mathematically predicted ephaptic mode of coupling as well as GJ coupling. These data suggest opportunities for novel anti-arrhythmic therapies targeting noncanonical conduction pathways in the heart.