The potential role of fall-seeded cover crops for weed management in edamame [soybean, Glycine max (L.) Merr.] is unknown. Field experiments were conducted over three edamame growing seasons to (1) determine the extent to which cover crop–residue management systems influence edamame emergence while selectively suppressing weed density and biomass, and (2) determine whether cultivars differed in emergence in cover crop–residue management systems. Cover crop treatments included a winter-killed oilseed radish (Raphanus sativus L.), two canola (Brassica napus L.) treatments (early-killed and late-killed), two cereal rye (Secale cereale L.) treatments (early-killed and late-killed), and a bare-soil control. Two spring timings of a cover crop burndown application created the early-killed and late-killed treatments for canola and cereal rye. Twelve soybean cultivars were tested, including 11 edamame cultivars differing in seed size and a grain-type soybean control. Spring residue biomass in cover crop treatments ranged from 438 kg ha−1 for winter-killed radish to 9,003 kg ha−1 for late-killed cereal rye. Cultivars responded similarly to cover crop treatments, and with the exception of late-killed cereal rye, cover crop treatments resulted in similar crop emergence as the bare-soil control. While all cover crop treatments reduced weed biomass 6 wk after planting compared with the bare soil, winter-killed radish and both canola treatments increased weed density. Early-killed cereal rye has potential for weed management in edamame, as evidenced by the fact that the treatment did not interfere with planting or crop establishment, yet reduced weed density 20% and suppressed early-season weed growth 85%.