Police said that the woman had been attacked after she accepted a lift by three men in a truck in Manali, a resort town in the state.
No arrests have been made but police have set up roadblocks and are searching for the suspects.
Scrutiny of sexual violence in India has grown since the rape and murder of a student on a Delhi bus in December.
The gang rape of the student sparked widespread protests and prompted the government to alter laws relating to rape in India.
Five men and one juvenile have been charged with the rape. One of the men has since hanged himself in prison, officials say.
In the Manali case, police say the three men drove the woman to a secluded spot where they raped her and robbed her.
After arriving in Manali on Monday she had been on a visit to Vashisth, a nearby tourist area popular with foreigners, but was delayed and had been looking for a taxi in the early hours of Tuesday morning.
"Because it happened at night, she couldn't read the truck number. At around 7am, we put up checkpoints everywhere and we've been looking for the suspects," senior local police official Vinod Dhawan told BBC Hindi.
"We have found some clues at the crime scene."
A case of rape was filed after the woman had been medically examined in a local hospital, police say.
The US embassy in Delhi said it was aware of the case. "We are in contact with authorities but due to issues of privacy we have no further comment," a spokesperson told the BBC.
The attack comes after a Swiss tourist was gang raped in Madhya Pradesh state in March - six men were arrested in connection with that attack.
That same month, India passed a new bill containing harsher punishments, including the death penalty in certain cases, for rapists.
Reported cases of sexual assault are on the rise in India, although foreign tourists are rarely targeted.
Indian police say that a 30-year-old American woman has been gang-raped in the northern state of Himachal Pradesh.