More than 700 people were believed to be attending the outdoor concert.
"There was a sudden, loud screaming, and when I turned it looked as if people were being sucked down into a hole," one witness told YTN.
A woman standing nearby said a great "cloud of dust" billowed up from the ventilation shaft after the grate collapsed.
Most of the dead and injured were believed to be students, YTN said, adding that the concert organisers had repeatedly urged the spectators to move off the grate before it collapsed.
South Korea has suffered a recent series of catastrophic accidents involving young victims, including the sinking of the Sewol ferry in April that left more than 300 dead, most of them high school students.
In February, the roof caved in on a student-packed auditorium near the southern city of Gyeongju, killing 10 people and injuring more than 100. An investigation uncovered evidence of structural flaws and lax management controls.
The Sewol disaster prompted government promises of a national review of safety standards, as it became clear that poor regulatory oversight was a major contributor to the scale of the tragedy.
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