Four Union flags were removed from the war memorial in Kilrea in the early hours of Sunday morning.
The local Orange District is responsible for the decoration of the war tribute ahead of the Twelfth, and has vowed to replace the flags immediately.
An Orange spokesman said: “This was a deplorable act carried out under the cover of darkness. Such war tributes should be sacrosanct and those responsible ought to be ashamed of their actions.
“Their wickedness is deeply offensive not only to Unionists, but the wider community in Kilrea and the surrounding area, and more so the memory of those who fought in two World Wars.”
He added: “While these flags will quite rightly be replaced, we would appeal for anyone with information regarding this incident to contact police immediately.”