From the article:
The move comes less than a year after the companies announced plans to set up the facility in Prime Minister Narendra Modi's home state of Gujarat.
Some analysts say it marks a setback to the nation's technology industry goals.
However, a government minister says it will have no impact on the country's chip making ambitions.
Taiwan-headquartered Foxconn told the BBC that it will now "explore more diverse development opportunities".
The firm also said the decision was made in "mutual agreement" with Vedanta, which has assumed full ownership of the venture, but did not give details on why it withdrew from the deal.
"We will continue to strongly support the government's 'Make in India' ambitions and establish a diversity of local partnerships that meet the needs of stakeholders," Foxconn added.
New Delhi-based Vedanta said it had "lined up other partners to set up India's first [chip] foundry".
"The surprise pull-out of Foxconn is a considerable blow to India's semiconductor ambitions," Paul Triolo from global advisory firm Albright Stonebridge Group told the BBC.
"The apparent cause of the pull-out is the lack of a clear technology partner and path for the joint venture," he added. "Neither party had significant experience with developing and managing a large-scale semiconductor manufacturing operation."
However, Rajeev Chandrasekhar, India's Minister of State for Electronics and Information Technology, said on Twitter that Foxconn's decision had "no impact on India's semiconductor fab[rication] goals. None."
Mr Chandrasekhar added that Foxconn and Vedanta were "valued investors" in the country and "will now pursue their strategies in India independently".
The Indian government has been working on strategies to support the chipmaking industry.
Last year, it created a $10bn fund to attract more investors to the sector, in a bid to become less reliant on foreign chipmakers.
Prime Minister Modi's flagship 'Make in India' scheme, which launched in 2014, is aimed at transforming the country into a global manufacturing hub to rival China.
In recent years, several other firms have announced plans to build semiconductor factories in India.
Last month, US memory chip giant Micron said it would invest up to $825m to build a semiconductor assembly and test facility in India.
Micron said that the construction of the new facility in Gujarat will begin this year. The project is expected to directly create up to 5,000 roles, and another 15,000 jobs in the area.