How the century-old gilded bronze sculpture was taken remains unclear, but police say witnesses reported seeing two men with a ladder in the area earlier this month.
Bahlsen's has offered euro1,000 ($1,350) for information leading to the golden cookie's return.
A police statement said a local newspaper received a picture Tuesday showing someone in an outfit similar to Sesame Street's Cookie Monster character holding a golden cookie.
The sender wrote to demand that cookies be delivered to children at a city hospital.
Police aren't sure if the writer is the real cookie-statue thief, or someone who'd like to take credit.