The happy couple, known only as Sandra and Sarah, followed Hindu rituals during the ceremony which was conducted by a priest at the Mahadeva Shiva temple close to the Taj in the town of Agra.
After exchanging garlands, Sandra, 19, marked the head of 18-year-old Sarah with vermilion. They then made seven circuits around a fire in the traditional marriage custom.
The priest, Dharm Das, initially refused to "marry" the pair but relented after they gave an offering to the temple and said they would be his life-long disciples, reports said.
"Although the Hindu system of marriage doesn't allow such relationships or marriages, I am impressed with the love that the two women have for the monument of love," Das told the Mail Today.
"They had also argued that their Swedish society allows such kind of marriages."
Current Swedish law allows for same-sex couples to register civil partnerships, but stops short of allowing homosexual marriages outright. The government is currently considering a new legislative proposal which would give same-sex marriages equal footing with those between heterosexual couples.
The Taj Mahal was built by Emperor Shah Jahan in memory of his second wife Mumtaz Mahal who died giving birth in 1631.
At Saturday's "wedding", Sandra acted as the groom while Sarah played the role of the coy bride, newspapers reported.
"We were in love with each other since childhood," Sandra said. "A few months ago we came to Agra and were mesmerized by the Taj Mahal.
"Both of us had read extensively about the emperor and his love and decided to draw a parallel and get married in the proximity of the Taj."
The couple lives together in New Delhi working for a children's charity, reports said.
The priest said the ceremony had attracted much local curiosity as homosexuality is illegal in India.
"Since it was practically a once-in-a-blue moon event in Agra, a large number of people gathered outside the temple for a glimpse of the couple," he said.
One priest told the Times of India that "foreigners are mocking our system and misusing the liberal parameters. Such waywardness must be stopped."