Gilroy police said that they were searching for a possible second suspect at and around the Festival site, 48 kilometers southeast of San Jose in California.
The gunman was described by a witness as a white man in his 30s armed with a rifle who opened fire indiscriminately.
Police chief Scott Smithee said the suspect may have managed to escape metal detectors and bag searches at the Festival entrance, by breaking through fencing around the site.
People were injured in the rush to get away from the scene as they started hearing the gunshots.
Music bands entertain the almost 100,000 people who are reported to attend the popular, family-oriented event to take part in or watch cooking competitions.
Governing gun-use and abuse
California's governor Gavin Newsom said the incident was "horrific."
US President Donald Trump earlier tweeted that law enforcement officers were at "the scene of shootings" in Gilroy, urging members of the public to "Be careful and safe!"
Similar gun rampages and their tragic consequences have raised awareness about accessibility of firearms in the US today.
In 2018, 17 people were killed at a high school in Parkland in the state of Florida, which gave fresh impetus to call for tighter gun laws.
Firearm control is a polemic issue in the US, pitching those who support the possession of guns, and those who consider regulations are too lax and lead to incidents like the latest one on Sunday in Gilroy.
Efforts to address gun control in the US legislature have been largely deadlocked at the federal level. However, earlier this year the members of the House of Representatives passed federal legislation, HR8 that requires federal background checks for all firearms sales year. The measure has been described as largely symbolic given the continued predominance of the Republican party in government in the Senate.