Swaraj, who left by an early morning Air India flight, tweeted, "Leaving for New York."
The International Yoga Day event will be attended by UN Secretary General Ban Ki-moon among others. The United Nations had in December last year declared June 21 as International Yoga Day.
The proposal had been mooted by Prime Minister Narendra Modi during his first address to the UN General Assembly in September last year.
Swaraj is battling a controversy over helping scam-tainted former IPL Chief Lalit Modi, who is facing money laundering and other charges, get travel papers in Britain, with the Opposition demanding her removal.
Aam Aadmi Party activists today protested outside Swaraj's residence in New Delhi, demanding her resignation.