Symbiont genotype plays a vital role in the ability of a coral host to tolerate rising ocean temperatures, with some members of the family Symbiodiniaceae possessing more thermal tolerance than others. While existing studies on genetic structure in symbiont populations have focused on broader scales of 10–100 s of km, there is a noticeable gap in understanding the seascape genetics of coral symbionts at finer—yet ecologically and evolutionarily relevant—scales. Here, we mapped short reads from 271 holobiont genome libraries of individual Acropora hyacinthus colonies to protein coding genes from the chloroplast genome to identify patterns of symbiont population genetic structure. Utilizing this low‐pass method, we assayed over 13,000 bases from every individual, enabling us to discern genetic variation at a finer geographic scale than previously reported at the population level. We identified five common Cladocopium chloroplast SNP profiles present across Palau, with symbiont structure varying between Northern, mid‐lagoon, and Southern regions, and inshore–offshore gradients. Although symbiont populations within reefs typically contained significant genetic diversity, we also observed genetic structure between some nearby reefs. To explore whether coral hosts retain their symbionts post‐transplantation, we experimentally moved 79 corals from their native reefs to transplant sites with both different and similar chloroplast SNP profiles. Over 12 months, we observed 12 instances where transplanted corals changed profiles, often transitioning to a profile present in adjacent corals. Symbiont genetic structure between reefs suggests either low dispersal of symbionts or environmental selection against dispersers, both resulting in the potential for significant adaptive differentiation across reef environments. The extent to which local corals and their symbionts are co‐adapted to environments on a reef‐by‐reef scale is currently poorly known. Chloroplast sequences offer an additional tool for monitoring symbiont genetics and coral–symbiont interactions when assisted migration is used in restoration.