The flag mistake came as the players were introduced in the stadium before the start of a women's soccer match between North Korea and Colombia on the first day of competition at Hampden Park in Glasgow, Scotland.
The North Korean squad walked off when South Korea flags were displayed next to their players in a video package on the stadium's big screen accompanying the introductions. The start of the match was delayed for about an hour.
North and South Korea are bitter enemies and technically still at war even though an armistice ended the 1950-53 Korean conflict.
"Our team was not going to participate unless the problem was solved properly," North Korean coach Sin Ui Gun told the BBC after the match. "Unfortunately it took some time later for the broadcast to be done again properly and we made the decision to go on with the match."
A London 2012 spokesman said organizers were very upset.
"A genuine mistake was made for which we apologize," spokesman Andy Mitchell said.
"Clearly it was an embarrassment," British Olympic Association chairman Lord Colin Moynihan added.
North Korea won the match 2-0.