The woman, reportedly from Lausanne, was on a biking holiday with her husband in central Madhya Pradesh state when she was attacked on Friday night while putting up a tent in a remote forested area.
Her husband was tied up as she was assaulted and the pair were also robbed, police said on Sunday.
Local officer M.S. Dhodee said five local men, illiterate small-scale farmers aged 20 to 25, had been arrested.
A sixth suspect, 19, was detained in neighbouring Uttar Pradesh state and was being returned to the area.
Dhodee said they had recovered a laptop, some cash and a mobile phone stolen during the assault, which occurred as the couple were getting ready to spend the night ahead of a trip to the Taj Mahal in the town of Agra.
"They were passing by, noticed the couple putting up their tent and saw an opportunity to attack and rape the woman," Dhodee said.
"We found the laptop buried carefully under a pile of leaves, near some shrubs in the forest," he said.
"The mobile phone was recovered from the home of the mother-in-law of one of the men."
The five arrested men face charges of rape and robbery.
The sixth suspect is expected to face the same charges.
Their confessions to police will likely be inadmissible as evidence under Indian law, which rarely allows court prosecutors to cite such statements since they are seen as unreliable and involuntary.
The alleged rapists live in a village near the scene of the assault, which took place about 40 miles (70 kilometres) from the nearest town of Gwalior, which is about 180 miles south from New Delhi.
After the attack, the 39-year-old rape victim and her husband, a 30-year-old mechanic, stopped a motorcyclist who took them to the nearest police station, said SonntagsBlick, a Swiss German-language newspaper.
She underwent a medical examination at a local hospital before leaving for the Indian capital Delhi, police said.
The woman's mother-in-law told AFP in Switzerland that she had spoken to her son and the couple were recovering.
"This morning he phoned me to say they are in New Delhi and that they are both alright," she said in a phone interview from the family's farm in central Switzerland.
U.C. Shadangi, another local police officer, said that his force was in touch with the Swiss embassy who declined to comment to AFP about the case.
The couple arrived in Mumbai last month after visiting Iran and began a cycling holiday across India, making their way to Orchha, a popular foreign tourist haunt in Madhya Pradesh on Thursday, police said.
The Swiss foreign ministry in Bern released a statement on Saturday expressing deep shock at the "tragic incident".
The ministry had issued an advisory for Swiss nationals travelling in India last month, warning that sexual violence was on the rise across the country, and urging both women and men to travel in large groups and with local guides.
In January, a South Korean student holidaying in Madhya Pradesh said she had been raped and drugged by the son of the owner of the hotel where she stayed.
That incident came just six weeks after thousands took to India's streets in nationwide protests following the fatal gang-rape of a 23-year-old student on a bus in New Delhi.
The victim, a physiotherapy student died from internal injuries after being savagely assaulted by six men.
One of her alleged attackers was found dead in his prison cell in New Delhi on Monday.
Police suspect he hanged himself, but his family says he was murdered.
The government has since opened an investigation into his death.
India's government is facing heavy pressure to step up efforts to protect women after the deadly gang-rape in the capital last December.
Under a new bill approved by India's cabinet last week, rapists face a minimum 20-year jail term and the death penalty if the victim dies from injuries or is left in a persistent vegetative state.