Alex Salmond is also expected to make an announcement about Scotland forming closer ties with India in areas such as business and tourism.
The trip will run until Thursday's closing ceremony, during which the official handover of the Games to Glasgow will take place.
The city is due to host the next Commonwealth Games in 2014.The Scottish government said the first minister would visit the athletes' village to meet members of Team Scotland.
Officials said Mr Salmond would also announce "significant" Indian investment and job creation in Scotland and hold "high level" ministerial meetings with the Indian government.
Mr Salmond said: "Our athletes are performing fantastically well in Delhi, all of Scotland is behind them, and I am proud to attend the Commonwealth Games to show support for their achievements.
"I would also like to wish the Scottish cast at the closing ceremony the best of luck.
"They will be great ambassadors for the country as Scotland assumes host nation status."
Mr Salmond said Scotland already had very strong ties with India.'Emerging markets'
He added: "We have one of the most thriving Asian communities in the world - food, the arts, business and religious tolerance and diversification have all benefited enormously from the 35,000 Indian people who call Scotland home.
"As an emerging global economic power, India is an essential partner for Scotland."
The first minister said 11 Indian companies had made investments of £700m in Scotland during the past five years, employing more than 3,200 people.
An estimated 4,000 Indian students also study at Scottish colleges and universities.
Lena Wilson, chief executive of Scottish Enterprise, said there were "tremendous opportunities" for Scottish companies to develop trade and investment partnerships with their Indian counterparts.
VisitScotland's chief executive Malcolm Roughead said this week presented an opportunity to showcase Scotland on a world stage.
He said: "Tourism from India is worth around £15m to Scotland and is one of the emerging markets with greatest growth potential.
"Engaging with travel agents, trade contacts and the media face-to-face in India will allow us to capitalise on this potential."
Source: bbc.co.uk
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