The story is set in 1965, on an idyllic New England island called "New Penzance". Twelve-year-old Sam Shakusky (Jared Gilman) is an orphan who is attending a "Khaki Scout" summer camp, Camp Ivanhoe, led by Scout Master Ward (Edward Norton). Suzy Bishop (Kara Hayward) lives on the island with her attorney parents — Walt (Bill Murray) and Laura (Frances McDormand) — and three younger brothers in a house called Summer's End. Sam and Suzy met the previous summer during a church performance of Noye's Fludde by Benjamin Britten, and they remained pen pals over the following year. They made a secret pact to reunite the following summer and run away together. Sam brings camping equipment, and Suzy brings six books, her cat, and a record player. They spend several days hiking and camping together in the wilderness with the goal of reaching a secluded cove on the island, which they name Moonrise Kingdom. They dance on the beach and their young romance blossoms. Suzy's parents, the police, and the scout master eventually find them at the cove.

Suzy returns with her parents and is forbidden from seeing Sam again. Sam stays with police Captain Sharp (Bruce Willis) while they await Social Services (Tilda Swinton), who will place him in a "juvenile refuge" because his foster parents no longer wish to house him. The scouts, who previously were not kind to Sam, later decide it is their duty to help the young lovers run away again. Suzy, Sam, and the other scouts seeks out the help of Cousin Ben (Jason Schwartzman), an older relative of one of the scouts who works at the larger Khaki Scout summer camp, Fort Lebanon, run by Commander Pierce (Harvey Keitel). After many twists and turns, Sam and Suzy eventually are apprehended on a church steeple during a violent hurricane and flash flood, evoking the earlier references to Noah. The church steeple is destroyed by lightning, but everyone survives.

Sharp decides to become Sam's legal guardian, saving him from the orphanage and allowing him to remain on the island and be with Suzy. The last scene takes place at Summer's End, with Sam painting a landscape of the cove and then slipping out the window as Suzy and her brothers are called to dinner.