The flag flap began during player introductions when a North Korean player was introduced along with a shot of the South Korean flag.
The match against Colombia was delayed for more than an hour, and organizers apologized for the error.
"Today ahead of the women's football match at Hampden Park, the South Korean flag was shown on a big screen video package instead of the North Korean flag. Clearly that is a mistake," organizers said. "We will apologize to the team and the National Olympic Committee and steps will be taken to ensure this does not happen again."
The statement, however, included another gaffe: It failed to refer to the countries by their official Olympic names, causing organizers to reissue the statement using "Republic of Korea" and "Democratic People's Republic of Korea."
Commenting on the flap, the International Olympic Committee pointed to London officials.
"It's a matter for the organizers," IOC spokesman Mark Adams said.
North Korea won the match 2-0.
North Korea and South Korea are bitter rivals. The flag mix-up comes amid high tension on the Korean Peninsula following a North Korean long-range rocket launch in April and repeated threats by Pyongyang to attack the South. Seoul and the U.S. have called the launch a cover for a test of banned long-range missile technology. North Korea says the rocket, which broke apart shortly after liftoff, was meant to put a satellite into orbit.
Wednesday's match started 1 hour, 5 minutes late. Fans were confused at first, then turned to doing the wave and finally started booing as they became increasingly restless.
An announcement was eventually made over the public address system about 20 minutes after the scheduled 7:45 p.m. (1845 GMT; 2:45 p.m. EDT) kick off, apologizing for the delay and saying it "was due to an issue behind the scenes. We're trying to resolve it and we'll keep you updated."
To pass more time, music was pumped from the speakers. Players from both teams finally emerged onto the field about 40 minutes after the match was supposed to begin. The players warmed up again for 10 minutes before they returned inside the tunnel to be led out again for the national anthems.
Flag controversies aren't new at the Olympics. At the 1992 Barcelona Games, Michael Jordan, Magic Johnson and Charles Barkley from the Dream Team draped U.S. flags over their shoulders to hide a rival sponsor's logo on their jackets when they received their gold medals.
At the 2010 Vancouver Games, the Australians displayed a flag with a boxing kangaroo -- the mascot for the country's team -- in the athletes village, despite an International Olympic Committee rule that usually only permits official national flags to be displayed. The IOC eventually relented.
In 2000, sprinter Cathy Freeman caused a stir when she took a victory lap after winning the 400-meter final at the Sydney Games draped in the Aboriginal flag, which was not recognized as an official national flag by the IOC.
Also in 2000, North and South Korean athletes marched together at the opening ceremony of the Sydney Olympics under the unified Korea flag, sparking a standing ovation. But with relations deteriorating in the years since, each country insists on a separate flag.
Last month, there was another mix-up in Britain. British field hockey officials apologized to the South African women's team for playing the apartheid-era national anthem before one of its matches at the London Cup, a warm-up event for the Olympics.
The event's organizer, Great Britain Hockey, said it was an administrative mistake and offered a "full and unreserved apology."