A doctor at the private Goyal Hospital told AFP Friday that Clinton had undergone screening after suffering pain in her right hand following a fall.
The 70-year-old former presidential candidate was staying at Umaid Bhawan, the palace of the former royal family of Jodhpur in western Rajasthan state, now a spectacular heritage hotel.
"We did a CT scan and X-ray and found a hairline fracture around the wrist area. She was advised to take rest for few days and use a crepe bandage for support," said the doctor on condition of anonymity.
Local and international media quoted unnamed sources as saying Clinton had slipped in the bath in an accident that comes just five months after she broke her toe in London.
A few days earlier, video footage emerged showing Clinton stumbling on the uneven stairway of a 13th century Indian monument while holding the arm of an aide for support.