There were no reports of serious injuries from the accident that took place at 10:09am (0109 GMT) local time at an elementary school near the Futenma marine airbase.
The US military said it was taking the incident "extremely seriously" and was opening an investigation.
"This is a regrettable incident and we apologise for any anxiety it has caused the community," the military added in a statement, urging local residents to stay clear from where the object landed "for safety purposes".
The incident comes just two months after an American military chopper burst into flames after landing in an empty field in Okinawa.
Such accidents have sparked opposition to the US bases on the strategic island, which would be a launchpad for any American military activity in Asia.
"School children were taking a sports class on the field when the accident happened, but no one was injured seriously," a local police official told AFP.
The window that came off from the chopper measured about 90 centimetres in length and width, he said.
"My body is shivering with fear," a mother of one of the schoolchildren told private broadcaster TBS in front of the school.
Another angry mother said: "My kid was among those who were on the field and children could have died if it fell on the wrong part of the field."
The Futenma airbase is already a major source of mistrust between Japan's central government and Okinawa over a wider US military relocation programme signed between Tokyo and Washington in 1996.
Residents want Futenma to be closed and a replacement built elsewhere in another part of Japan or overseas, saying they can no longer live with the noise pollution, accidents and occasional crimes committed by US service members.
"This kind of incident causes worries among not only people at the school but all the people in Okinawa and should never happen," said chief Japanese government spokesman Yoshihide Suga.
A Japanese policeman stands guard at the entrance gate of the elementary school in Ginowan, Okinawa on December 13, 2017, where a window from a US military helicopter fell onto the school's sports ground.
A window from a US military helicopter fell onto a school sports ground in southern Japan Wednesday, the marines said, apologising for a "regrettable" incident likely to fuel opposition to their presence.
