Ten-year-old Sebastian went missing near the village of Wittdün on the eight-square-mile island of Amrum on Sunday. He was last seen at around 6pm, before his parents called the police at two hours later.
"We are now actively searching for the boy," police spokeswoman Kristin Stielow said on Tuesday. Around 40 officers are searching the entire island and the nearby coastline, while transport connections are being checked.
"We're also searching through the dunes, since a child could easily get lost there," Stielow added.
Sebastian has long, curly, blond hair and was wearing jeans, a multi-coloured horizontally striped T-shirt and a blue, long-sleeved fleece jumper when he was last seen on a "pirate ship" playground just 200 metres from his parents' holiday home. He was also barefoot.
Police are also trying to find another boy, named Lukas, who was seen with Sebastian before he disappeared. Police are calling on Lukas' family to get in touch with them as soon as possible.
Pictures of the ten-year-old have been released, and police are appealing for help. "We hope that everyone keeps a lookout for the boy," Stielow told Bild newspaper. "We cannot rule out that he is now on the mainland."
An accident is considered unlikely, since Sebastian was in no immediate danger at the playground, which was around a kilometre from a relatively safe stretch of shoreline.
"The beach is completely safe," rescue worker André Richter told Bild. "You can't really drown there. Even when the tide is in the water is only at knee height, and the tide was out when Sebastian disappeared."
Anyone with information has been asked to call the police on +49 4661 40110 or 110.