Tanveer Hussain arrived in the small village of Saranac Lake in New York state for the World Snowshoe Championships.
Police said he has been charged with sexual assault and endangering the welfare of a child.
He had garnered much attention before arriving for the championship after the US Embassy in New Delhi denied him and another athlete Abid Khan visas around the same time President Donald Trump had issued an order barring people from seven Muslim-dominant countries to the US.
Though India was not among the seven countries, the denial of visa was seen associated with the executive order.
Hussain was allowed a visa to enter the US for the competition following intense lobbying from local officials and residents in the Adirondacks, as well as by US Senators Kirsten Gillibrand and Charles Schumer.
Police arrested Hussain on Wednesday after the girl, who is under the age of 13, accused him of sexually abusing her, a report in the Adirondack Daily Entreprise said.
Police Sergeant Casey Reardon said the girl and her parents reported the abuse to police. It took place on Monday evening in the village. After the complaint, Reardon said police located Hussain who has been cooperating in the case, the report said.
Hussain was arraigned and his lawyer entered a not-guilty plea on Hussain's behalf.
"I could not have entered anything else but a not-guilty based on the information I had," his lawyer Brian Barrett said.
"Based on the limited communications I could have with Hussain, it did not allow for me to properly evaluate the case and make an informed decision on behalf of my client.
"They are merely allegations alone. Not only is he innocent, he is presumed innocent by law. That is how he should be seen in the community and by anyone paying attention in this case," Barrett said.
Hussain and Khan had planned to return home this week. It said "a visibly upset Hussain", with hands shackled and still wearing a maroon World Snowshoe Championships hat, pleaded with the judge not to send him to jail, the report said.
"Sir, please. Help me," Hussain said.
The judge decided not to accept a plea because he was not sure if Hussain fully understood the charges against him. He remanded him to the Essex County Jail in Lewis in lieu of $5,000 cash bail or $10,000 bond. A preliminary hearing on his case is scheduled for next Monday.