All five men admitted to the attack, which occurred Friday night as the woman and her husband camped out in a forest in Datia district of Madhya Pradesh state, said D. K. Arya, a senior police officer.
Arya said the men, who are from nearby villages, were arrested in Datia. Police were searching for two other men believed to have been involved in the attack, he said.
The couple told police that the woman had been raped by seven or eight men, but that it was dark and they could not be sure of the exact number, Arya said. They said the husband also was attacked by the men.
The woman, 39, was treated Saturday at a hospital in the nearby city of Gwalior and was released later that day, police said.
The couple were planning to travel later Sunday from Datia to the Indian capital of New Delhi, about 400 kilometers (250 miles) to the north, Arya said.
The attack came three months after the fatal gang rape of a woman aboard a New Delhi bus outraged Indians, and was front-page news in Indian newspapers on Saturday.
Prior to the attack, the couple, who were on a three-month vacation in India, had visited the temple town of Orchha and were planning to cycle to Agra to visit the Taj Mahal, nearly 210 kilometers (130 miles) away.
They set out from Orchha on Friday and pitched their tent in a forest near Jatia village when they were attacked by a group of men armed with wooden sticks, police said.
The men beat up the husband, tied him to a tree and then raped the woman, police said. They also stole the couple's cellphone, laptop computer and 10,000 rupees ($185). Police said they recovered the laptop and phone from one of the men who was arrested.
The Swiss ambassador in India, Linus von Castelmur, said he spoke with the couple and assured them of the Swiss government's help and support.
"Their health and treatment is the priority of the moment," the Swiss Embassy said in a statement.
The embassy said it was in touch with authorities in Madhya Pradesh and has urged a "swift investigation and for justice to be done."
Figures from India's National Crime Records Bureau show that a woman is raped every 20 minutes in India. However, many incidents of rape and other sexual crimes go unreported due to the stigma attached to such crimes in the conservative country. India's conviction rate for rapes and other crimes against women is among the lowest in the world.
Last month, the Swiss government issued a travel notice for India that included a warning about "increasing numbers of rapes and other sexual offenses" in the South Asian nation, and the latest incident could prompt other countries to issue similar warnings.
Travel industry representatives in India said the incident, coming so soon after the December gang rape in New Delhi, would affect tourism.
"Such incidents will definitely have a negative impact on tourism. It is very unfortunate," said Subhash Goyal, head of the Indian Association of Tour Operators.
According to government statistics, around 6.5 million foreign tourists visited India in 2011, generating about $120 billion for the nation's travel and hospitality sector.
The gang rape in December of a 23-year-old student aboard a moving bus in New Delhi set off nationwide protests, sparking a debate about the treatment of women in India and highlighting the inability of law enforcement agencies to protect them.
One of six suspects in the December attack was found dead in a New Delhi jail last week. Authorities said he hanged himself, but his family and lawyer insisted foul play was involved, and a magistrate is investigating. Four other men and a juvenile remain on trial for the attack.
The incident prompted the government to pass a law increasing prison terms for rape from the existing seven to 10 years to a maximum of 20 years. The law provides for the death penalty in extreme cases of rape that result in death or leave the victim in a coma. It has also made voyeurism, stalking, acid attacks and the trafficking of women punishable under criminal law.