They were ripped from the railings around the memorial, on Wellington Road, Bridlington at some time last night (Sunday).
They had been placed on the memorial to commemorate the hundredth anniversary of the First World War.
Insp Rob Cocker said: “This act of vandalism shows a complete lack of respect for those who fought and died for our freedom and I want to reassure the residents of Bridlington that it will not go unpunished.
“We are working hard to gather evidence to trace those responsible and would ask for anyone who can assist us to get in touch. The poppies that were removed have not yet been found. If you come across them or you saw someone carrying the flowers yesterday evening, please let us know. The information you provide could be vital in helping us to track down the culprits.”
If you have information, call 101, quoting log number 125 of October 22.