Police Inspector Sushant Gaur said Culpo and others in her group are accused of violating India's Heritage Act. Culpo, from Cranston, Rhode Island, was on a 10-day visit to India.
He said they shot a commercial for footwear at the Taj Mahal on Sunday without the permission of the state-run Archaeological Survey of India. Police acted on a complaint received from the ASI on Thursday, Gaur said.
If found guilty, they can be jailed for up to two years and fined 100,000 rupees ($1,600), Guar said.
Indian police file a case as a first step in investigating a complaint. They formally charge a suspect in court at the end of the investigation.
Indian media said commercial activity is banned on the premises of the Taj Mahal, a World Heritage Site.
Culpo posed for photographs wearing one sandal, holding another in her hand and keeping another pair on the bench she was sitting on, Guar said.
Culpo left India on Sunday night. A representative in India declined to comment.
Cuplo speaking to the Providence Journal of Rhode Island on Thursday, expressed regret over the photo shoot.
"I guess their vision was, 'What's better to identify India than the Taj Mahal?' But unfortunately it's something that was highly offensive. Honestly, I did say out loud at one point, 'Isn't this a little inappropriate?'" Culpo was quoted as saying on the newspaper's website.