"No suspect (s) in custody", said the office on Twitter.
Five of the victims are male and one victim is female, and they range in age from 20s to 70s.
Ron Lendvay, director of investigations for the Jacksonville Sheriff's Office, said several shots rang out about 12:35 p.m. Sunday on a boulevard in the stadium's general area and that five men and one woman were hit by gunfire. Deputies said the shooting did not affect fans at the game.
The incident was blocks from TIAA Bank Field, where the Jacksonville Jaguars were playing the Houston Texans.
The Jacksonville Sheriff's Office says the shooting could be gang related.
The vehicle then fled westbound on Pippin Street.
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The Australian ex-hacker sought asylum from Ecuador in 2012 to avoid extradition to Sweden. Assange was given sanctuary in the building by Moreno's predecessor Rafael Correa.
Authorities had no immediate report on what led up to the shootings.
Police said Jaguars fans who were parked near the shooting scene would be escorted to their vehicles by police.
Three people are in critical condition after the shooting, police said, according to the Jacksonville Sheriff's Office.
An update on the conditions of the wounded wasn't immediately available late Sunday and they were not identified by name.
Gov. Rick Scott tweeted that he spoke with Jacksonville Sheriff Mike Williams and offered any state resources the agency may need.