Contrary to early reports, no shots were fired during the fight at the Michael B. White Elementary School, the school district reported.
Cleveland police Commissioner Wayne Drummond said the fight began between two teenage girls who attended the ceremony, and spread to adults who had come to view the kindergarten graduation.
School district spokeswoman Roseann Canfora said no students at the school were involved in the fight.
The school was put on lockdown after the ceremony, The (Cleveland) Plain Dealer reported.