The fast food giant said it had received 130 complaints after handing out the tumblers to purchasers of "Value Sets", which included fries and a soft drink, during their "Olympic Cheer Coke Glass Campaign" in June and July.
McDonald's said they gave away six million tumblers in Japan, some of which had "glass protrusions" on their edges or insides because of a manufacturing error.
"We received 130 complaints from our customers by August 7, of which 78 customers said they suffered cuts, although injuries were not serious enough to warrant their going to hospital," company spokesman Kazuyuki Hagiwara told AFP.
He said flawed metallic moulds used by the producer of the glasses were to blame.
The company said customers who return their glasses between now and the end of October will be given replacements.
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