About 30 shots were fired in Clara Muhammad Square around 2:30 p.m. PPD Commissioner Kevin Bethel said.
Two groups exchanged "a large volley of gunfire," causing the crowd to panic, he told reporters.
Police stopped four armed suspects, three male and one female, and took them into custody, the Commissioner said. All but one of them are said to be "juveniles."
A police officer shot a 15-year-old boy in the leg and shoulder and then rushed him to the hospital, Bethel continued. He was also said to be armed.
Two others were shot during, including a 22-year-old man who was struck in the stomach and a juvenile who was hit in the hands, according to Bethel.
All three are said to be in stable condition.
Another child was accidentally struck by a police cruiser during the initial panic and suffered a fractured leg, the Commissioner said.
Some 1,000 people were gathered in and around the park to celebrate Eid al-Fitr, the festival marking the end of the fast of Ramadan.
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