The UK voted to leave the EU in a historic referendum on Friday, sending shockwaves across global markets.
India's Sensex fell by 3.4% to 26,022.60 points soon after the outcome of the vote became clear.
But Mr Jaitley said that India's market fundamentals are strong enough "to smooth this volatility".
The minister acknowledged however, that "Brexit" would cause financial uncertainties for India and other markets around the world.
"As I have often said, in this globalised world, volatility and uncertainty are the new norms. This verdict will, obviously, further contribute to such volatility not least because its full implications for the UK, Europe and the rest of the world are still uncertain," he wrote on his Facebook page.
But he added that India was "well prepared" to deal with "the short and medium term consequences of Brexit".
"The government and the Reserve Bank of India as well as other regulators are well prepared, and working closely together, to deal with any short term volatility," he said.
He added that "our aim will be to smooth this volatility" and minimise the "impact on the economy in the short term".
Mr Jaitley also said India can emerge as a "safe haven" for investors in these "turbulent times".
"India stands out both in terms of stability and of growth," he said.
Meanwhile, India's central bank chief, Raghuram Rajan, has said that India is capable of mitigating the "shock" of Brexit.
"If we can manage properly it will be a non-event. A larger question is to find places where we can put money going forward," he said.
Indian company Tata Sons, which operates 19 companies in the UK, said it was "committed to delivering long term value for all its stakeholders"
"Each company continuously reviews its strategy and operations in the light of developments, and will continue to do so. Access to markets and to a skilled workforce will remain important considerations," a spokesperson of the group said.

The money has been allocated from the Inverness Common Good Fund.
Highland Council has set aside £200,000 and Highlands and Islands Enterprise could provide £60,000 to the £360,000 project.
The rest of the 19th Century building would continue to be used as a sheriff court.
Finance Minister Arun Jaitley has said India is "well prepared" to deal with any volatility arising from the UK's decision to leave the European Union.
[NEXT_CONCEPT]
Funding of £100,000 has been approved for a project to turn Inverness Castle's North Tower and its look-out into a new tourist attraction.