Furrow-irrigated rice (Oryza sativa L.) hectares are increasing in the Midsouth. The lack of sustained flooding creates a favorable environment for weed emergence and persistence, which makes Palmer amaranth (Amaranthus palmeri S. Watson) difficult to control throughout the growing season. The negative yield impacts associated with season-long A. palmeri interference in corn (Zea mays L.), cotton (Gossypium hirsutum L.), and soybean [Glycine max (L.) Merr.] have been evaluated. However, there is limited knowledge of the weed's ability to influence rice grain yield. Research was initiated in 2022 and 2023 to determine the effect of A. palmeri time of emergence relative to rice on weed seed production and grain yield. Cotyledon-stage A. palmeri plants were marked every 7 d, beginning 1 wk before rice emergence through 4 wk after rice emergence. Amaranthus palmeri seed production decreased exponentially as emergence timing was delayed relative to rice, and seed production increased by 447 seed plant^–1 for every 1-g increase in weed biomass. Without rice competition and from the earliest emergence timing, A. palmeri produced 540,000 seeds plant^–1. Amaranthus palmeri that emerged 1 wk before the crop had the greatest spatial influence on rice, with grain yield loss of 5% and 50% at a distance of 1.4 m and 0.40 m from the weed, respectively. As A. palmeri emergence was delayed, the area of influence decreased. However, A. palmeri plants emerging 3.5 wk after rice emergence still negatively affected grain yield and produced sufficient seed to replenish the soil seedbank, potentially impacting long-term crop management decisions. These results show that the time of A. palmeri emergence is a crucial factor influencing rice grain yield and weed seed production, which can be used to determine the consequences of escapes in rice.