She arrived at the Devi Ahilya Bai Holkar Airport at around 8:00 pm in a private plane amidst tight security, an official said.
She left for Maheshwar, a town on the banks of the Narmada river in Khargone district a little later.
Ms Clinton is scheduled to visit the state's erstwhile Holkar kingdom, where apart from a boat ride along the scenic Narmada river, she would also watch the world renowned Maheshwari saree being weaved, an art started by Queen Ahilya Bai to help the downtrodden, an official said.
She would stay tonight at the Ahilya Fort Hotel in Maheshwar. This is a private visit, Khargone Collector Ashok Kumar Verma told PTI.
Tomorrow morning, Clinton would be in Dhar district where her itinerary includes a visit to Mandu, home to historical monuments frequented earlier by Mughal rulers, officials said.
She would return to Maheshwar in the evening and interact with children of a local school before halting for the night at the holy town, they added.
"She will visit the place where the famous Maheshwari sarees have been weaved for long. It is an art started by Ahilya Bai Holkar, the ruler of the kingdom, to help the downtrodden. She will also have a boat ride on the Narmada," Mr Verma said.
"On Tuesday morning, she will leave for Indore from where she will fly back," he added.
Maheshwar, some 91 kilometres from here, was the capital of the erstwhile Holkar kingdom till January 6, 1818, after which Indore was designated as the capital under the reign of Malhar Rao Holkar III.
The former US Secretary of State is in Maheshwar at the invitation of Richard Holkar, scion of the erstwhile Holkar kingdom.