The incident occurred Saturday at the Country Thunder event in Florence, The Arizona Republic reported.
Deputies working at the event received reports of an escalating argument between two groups of festival-goers.
When they arrived at the scene, they found a 36-year-old man, whose name was not released, with multiple stab wounds to his upper back and ribcage, an official said.
He was transported to a hospital where he was listed in critical condition.
Austin Hansen, 20, was arrested at the scene on suspicion of disorderly conduct and aggravated assault, officials said.
Country Thunder is a weekend-long annual country music festival that had more than 22,000 attendees this year, a festival spokesman said.
Saturday's headliners included Diamond Rio and Toby Keith.
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