The archipelago, known as Senkaku in Tokyo and Diaoyu in Beijing, has been at the centre of a political storm in recent days.
"The map has one set of islands for each country. Is this a message from Apple that we civilians must not get engaged in a pointless dispute?" wrote a Japanese blogger, according to AFP.
The new mobile software program, which replaces Google Maps in Apple's new iOS 6 operating system, has already attracted criticism for its mistakes. The app could not even locate Apple's flagship store in Sydney.
One user tweeted: "Apple Maps app show the disputed Pacific islands belonging to Japan. Google show them as Chinese. Maybe a Chinese boycott of iPhone5?"
A number of users have taken to cyberspace to poke fun at the new maps, posting screenshots of bad mapping errors on blogs.
"It's a complete failure. It's slower, its directions are poorer and its location data doesn't seem to be accurate. All around, it's not quite there yet," a user interface designer for a San Francisco-based startup, Jeffrey Jorgensen, told the Associated Press.
Apple has admitted the errors and has assured users that it is working hard to fix them.