The women are from the Indian state of Arunachal Pradesh – which China claims as its own territory.
They are in a group due to compete in the Asian Games, which open in the Chinese city of Hangzhou on Saturday.
But India said they were prevented from travelling and accused Beijing of denying them the proper accreditation.
China has denied this, saying all athletes with legal documents are welcome.
According to Indian media, the three wushu athletes – Nyeman Wangsu, Onilu Tega and Mepung Lamgu – were left behind after their documents could not be downloaded.
None of the team’s other members reportedly experienced any problems.
In a statement, India’s foreign ministry said China had “discriminated” against the athletes in a “targeted and pre-meditated manner”.
“India firmly rejects differential treatment of Indian citizens on the basis of domicile or ethnicity,” it reads.
“Arunachal Pradesh was, is and always will remain an integral and inalienable part of India.”
India added it had launched a “strong protest” over the issue and said the country’s sports minister had cancelled his trip to the Games.
An official for the Olympic Council of Asia (OCA) said China had issued the women visas but they had refused to accept them as they were different to the visas given to the rest of the Indian delegation.
“According to the Chinese government regulations, we have the right to give them a different kind of visa,” said Wei Jizhong.
Another OCA official said the organising committee for the Games was working to find a solution so the women could compete.
It is not the first time there has been a dispute over documentation.
The same athletes did not compete at the World University Games in another Chinese city, Chengdu, in July because they were given stapled visas.
These visas are regarded as an indication that China does not accept India’s territorial claim over Arunachal Pradesh.
Beijing instead claims the area as “South Tibet” – which India firmly rejects. India claims the Aksai Chin plateau in the Himalayas, which is controlled by China.
A spokeswoman for China’s foreign ministry said on Friday that Beijing “welcomes athletes from each country to come to Hangzhou with legal documents to participate in the Asian Games.”
“The Chinese government has never recognised the so-called Arunachal Pradesh. The south Tibetan region is part of China’s territory.”
The source of the tension between the neighbours is a disputed 3,440km (2,100 mile) de facto border along the Himalayas – called the Line of Actual Control, or LAC – which is poorly demarcated. The presence of rivers, lakes and snow caps means the line can shift in places.
India also claims the Aksai Chin plateau in the Himalayas, which is controlled by China.
Soldiers on either side come face to face at many points, which can spark tensions – the last time being in December when Indian and Chinese troops clashed along the border in the town of Tawang.
The Asian Games are the continent’s biggest sporting event and are held every four years. They were due to be held in 2022 but were delayed due to the Covid pandemic.