However, shares in other major applicants that did not get licences at this stage slumped, with LIC Housing Finance falling as much as 6.7 percent and L&T Finance Holdings Ltd sinking 10.5 percent. Some analysts warned that the RBI could go slow in granting more approvals.
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The other company to receive a licence from the Reserve Bank of India on Wednesday, microfinance firm Bandhan Financial Services, is not listed.
Analysts said IDFC would likely benefit in the long-term given the opportunities for expansion in a country where about half of its 1.2 billion people do not have access to formal banking services.
Shares in the financial firm had already surged 21 percent since the RBI started reviewing bank licence applicants in November, as of Wednesday's close, given IDFC's perception as one of the frontrunners to get the approval.
However, analysts cautioned that IDFC's profitability in the near-term would likely be impacted. The RBI gave both IDFC and Bhandan 18 months to fully comply with central bank regulations before receiving final bank licence approval.
"We expect some run-up in stock price for IDFC in (the) immediate term, though upside is likely to be capped given operational challenges," Edelweiss said in a note dated April 2.
During the probation period, IDFC will need to meet all operational and compliance requirements for Indian lenders, including bearing the cost of setting up branches.
The approval of IDFC and Bhandan marks the start of a cautious experiment for a sector dominated by lethargic state lenders, many of which are reluctant to expand into rural areas or towns where banking penetration is low.
No new Indian bank has been formed since Yes Bank in 2004.
Shares in other companies hopeful of a bank licence slumped. The central bank said a total of 25 applicants were considered at this stage, and it would continue the process of approvals on a regular "on-tap" basis.
However, analysts warn that the next approval could take a while as the RBI on Wednesday made clear it would move conservatively. Issuing new bank licences has atracted plenty of criticism given concerns about whether companies can strictly separate their retail banking operations from their main businesses.
India's general elections are set to conclude in May. The Bharatiya Janata Party, which is leading in opinion polls, has not clarified its stance on the expansion of the banking sector.
"On-tap approvals are highly unlikely because we will have a new government soon, and who knows what policies they might have," said Phani Sekhar, a fund manager at Angel Broking.
IDFC shares were up 1 percent, while LIC Housing shares were down 1 percent and L&T Finance stock was down 9 percent at 0654 GMT. The benchmark BSE index was down 0.5 percent.