The comments come after China's central bank this month devalued the yuan, sparking concerns that policy makers were aiming to help struggling exporters - a scenario they feared would ignite a "currency war."
The rupee has fallen more than 2 percent against the dollar since the yuan devaluation, slumping at one point to its weakest since September 2013, when India was in the midst of its worst currency turmoil in more than two decades.
The outlook on emerging Asian currencies in the past two weeks also deteriorated to its worst in years, as bearish bets on the Chinese yuan hit their largest in more than five years after the surprise devaluation, a Reuters poll showed on Thursday.
Although Rajan added he did not believe the actions from the People's Bank of China were an indication of a long-term devaluation, he warned of the dangers.
"I think if the Chinese depreciation holds to about this level, it's not something that one should be overly concerned about," Rajan said at a banking event in Mumbai.
"If it's part of a process of getting competitive advantage through ... longer term depreciation it has to be worrisome across the world, partly because you could have tit-for-tat actions," he added.
Rajan, a former chief economist for the International Monetary Fund, has repeatedly warned about the dangers of competitive devaluations for emerging markets such as India.
Without naming examples, he expressed concerns that there were already such devaluations taking place over the past few years.
"Across the globe because of weak demand we have seen significant efforts to depreciate one's currency," he said on Thursday.
"That's a worrisome trend across the globe because there is only so much global demand and if we all are trying to capture it by depreciating our currency then it becomes a free for all."