Many tropical habitats experience pronounced dry seasons, during which arthropod food availability declines, potentially limiting resident and migratory animal populations. In response to declines in food, individuals may attempt to alter their space use to enhance access to food resources, but may be socially constrained from doing so by con‐ and heterospecifics. If social constraints exist, food declines should result in decreased body condition. In migratory birds, correlational evidence suggests a link between body condition and migration timing. Poor body condition and delayed migration may, in turn, impact fitness in subsequent seasons via carry‐over effects. To determine if winter food availability affects space use, inter‐ and intraspecific competition, body composition (i.e., mass, fat, and pectoral muscle), and migration timing, we experimentally decreased food availability on individual American Redstart (Setophaga ruticilla) territories in high‐quality mangrove habitat. Redstarts on control territories experienced ~40% loss of food due to the seasonal nature of the environment. Redstarts on experimental territories experienced ~80% declines in food, which closely mimicked natural declines in nearby, low‐quality, scrub habitat. Individuals on food‐reduced territories did not expand their territories locally, but instead either became non‐territorial “floaters” or remained on territory. Regardless of territorial status, food‐reduced American Redstarts all deposited fat compared to control birds. Fat deposits provide insurance against the risk of starvation, but, for American Redstarts, came at the expense of maintaining pectoral muscle. Subsequently, food‐reduced American Redstarts experienced, on average, a one‐week delay in departure on spring migration, likely due to the loss of pectoral muscle. Thus, our results demonstrate experimentally, for the first time, that declines in winter food availability can result in a fat–muscle trade‐off, which, in turn, delays departure on spring migration. Previous work has demonstrated that, for each day delayed after the first male arrival on the breeding grounds, American Redstarts experience an 11% decrease in the chance of successfully reproducing. Therefore, such delays in departure likely lead to fitness costs for migratory birds. Because tropical seasonal forests are expected to become drier in response to global climate change, Neotropical migratory bird populations may experience significant winter food limitation, further exacerbating population declines in the coming decades.