The meals, called Happy Sets in Japan, were meant for children.
They came with a toy, such as a tiny plastic Pikachu, and a Pokemon card and sold out in a day, according to Japanese media reports.
Mounds of wasted food were found near the stores.
“We do not believe in abandoning and discarding food,” the company said in a statement.
“This situation goes against our longtime philosophy that we have cherished as a restaurant to ‘offer a fun dining experience for children and families’.
“We sincerely accept that our preparations had not been adequate.”
McDonald’s said it was working on ways to prevent such a situation from happening again, such as limiting the number of meals each person can buy and ending online orders.
It said it might deny service to customers who fail to abide by the rules.
“We vow to return to the basics of what lies behind the Happy Set, which is about helping to bring smiles to families so we can contribute to the wholesome development of the hearts and bodies of children, who are our future,” the company said.
Collecting Pokemon cards is popular among adults and children in many places, with the most popular cards selling for $US1000 ($1500) or more.
Unusually large crowds were seen flocking to McDonald’s stores when the meals with Pokemon cards went on sale.
The cards were later being resold for up to tens of thousands of yen online.
McDonald’s has been selling Happy Meals for more than 40 years. In Japan, they usually sell for 510 yen ($5.29).
