Hirsch, 29, was charged with aggravated assault, which is punishable by up to five years in prison and a $5,000 (£3,200) fine, and is also facing a misdemeanour count of intoxication.
County prosecutor Ryan Stack said the woman, Daniele Bernfeld, was an executive for Insurge Pictures, a Paramount Pictures subsidiary.
Court documents say the incident happened on January 25 at Tao Nightclub in Park City, Utah, when Hirsch, looking drunk, approached Ms Bernfeld and asked why she looked “so tough”.
He also said she was a “rich kid who should not be at Sundance”, the documents say.
Investigators say Hirsch grabbed Ms Bernfeld and she pushed him away. He left but later came back and grabbed her from behind, the documents state.
She was put in a chokehold and pulled across the table before Hirsch landed on top of her on the floor, authorities said.
Ms Bernfeld told police she saw things going dark and might have blacked out momentarily.
Hirsch, of Encino, California, told police he did not know Ms Bernfeld but was having an argument with her.
He said he had three to four drinks and an officer told prosecutors h was slurring his words and smelled of alcohol.
Hirsch, best known for his starring role in Into The Wild, also appeared in Universal’s US Navy SEAL drama Lone Survivor, Peter Berg’s account of a disastrous 2005 military operation in Afghanistan.
He was at Sundance for the premiere of the drama Ten Thousand Saints, a film in which he appears alongside Ethan Hawke and Asa Butterfield. Hirsch will make his first court appearance on March 16 in Park City.