Brindisi prosecutors said he was also accused of "aggravated personal injury and crimes committed to the prejudice of a young foreign woman".
The ANSA and AGI agencies also report Mr Haggis has denied the allegations via his lawyer, Michele Laforgia.
The BBC has contacted Mr Haggis's representatives and the prosecutors.
"Make enquiries as soon as possible, I am totally innocent," the Canadian filmmaker said, according to the agencies, who quoted Laforgia.
Another lawyer representing Mr Haggis, Priya Chaudhry, issued a statement to various outlets including Variety, saying the director was"totally innocent".
Film festival in Italy
"Under Italian Law, I cannot discuss the evidence," she said.
"That said, I am confident that all allegations will be dismissed against Mr Haggis. He is totally innocent and willing to fully cooperate with the authorities so the truth comes out quickly."
Haggis, 69, who wrote and produced the Oscar-winning 2005 film Crash, was expected to headline the Allora Fest film festival, which kicks off on Tuesday in the city of Ostuni in the province of Brindisi.
Prosecutors said the alleged victim had been staying with Haggis ahead of the festival.
"The suspect allegedly forced the young woman, whom he met some time ago, to undergo sexual intercourse," they wrote.
Following one encounter, the woman was "forced to seek medical care", they added.
According to Italy's La Repubblica newspaper, Mr Haggis is under house arrest at a hotel in Ostuni.
The Allora Fest said they "learned with dismay and shock the news that Paul Haggis is in custody for alleged violence."
It added that the festival's directors "immediately proceeded to remove any participation of the director from the event."
Haggis is also known for writing and producing the film Million Dollar Baby, which also won a best picture Oscar, the year before Crash.
His other credits include writing the scripts for Bond films Casino Royale and Quantum of Solace.