Police said seven were taken to hospital with non-life threatening injuries and some others were treated at the scene.
Video shared with Reuters showed people trying to run to safety, climbing over event barriers.
Police, at the outset of the incident, received a report of a man with a gun at a park, Washington police Commander Guillermo Rivera told reporters. But police did not find any evidence of shots fired, Rivera said.
Washington Deputy Mayor Kevin Donahue had earlier said on Twitter that people in the city’s Dupont Circle were injured “running from what they thought were gunshots” but that there was no active shooter.
A man was later arrested when police found a firearm near him, officials said.
(Production: Nur-Azna Sanusi)