The prince came under heavy criticism after photographs appeared in the Sun, showing him wearing a German desert uniform with a swastika armband.
A written statement from Clarence House, Prince Charles' household, read: "Prince Harry has apologized for any offense or embarrassment he has caused. He realizes it was a poor choice of costume."
The photograph, which appeared under the headline "Harry the Nazi," was taken at the weekend at a friend's birthday party. The fancy dress theme was "colonial and native."
However Jewish groups and British Conservative Party leader Michael Howard said the prince should apologize in person.
"This was a shameful act displaying insensitivity for the victims, not just for those soldiers of his own country who gave their lives to defeat Nazism, but to the victims of the Holocaust," Rabbi Marvin Hier, founder of the Simon Wiesenthal Center, told the BBC.
Harry should go to the Nazi death camp Auschwitz to see for himself "the results of the hated symbol he so foolishly and brazenly chose to wear," Hier said.