The news of the royal's deployment earlier this year was initially kept secret due to a news blackout pact agreed to by British media in an effort to protect the prince and his fellow troops.
The blackout was first broken by an Australian magazine, then picked up by Matt Drudge's popular Drudge Report Web site.
The Daily Telegraph newspaper said the mayor's call for an apology follows a motion proposed by Councilor James Evans, which was unanimously backed by the council of the Royal Borough of Windsor and Maidenhead.
"There was no public interest in exposing details of Prince Harry's deployment, all it did was put the lives of British troops -- many of whom are based in our town -- at risk," Evans said.
Although the violation of the media blackout was widely criticized, Drudge has refused to apologize for reporting the story.
"Matt Drudge should apologize immediately for what he has done, and we would urge other journalists to remember that what they print has a direct impact on areas of conflict. Our military needs and deserves our support," Evans said.