Swaraj will be in New York for around a week, during which time she and her delegation of top Indian officials will hold about 20 bilateral and trilateral meetings with leaders attending the session.
The external affairs minister will address the United Nations General Assembly on Saturday, following which she will return to India.
The General Assembly of the 193-member UN comes against the backdrop of a humanitarian crisis in Myanmar that has forced hundreds of thousands of Rohingya Muslims to flee the country into neighbouring Bangladesh.
The crisis has touched India too; according to government estimates, around 40,000 Rohingya Muslims are illegally staying in the country. The top UN human rights official previously 'deplored' New Delhi's position that India would deport Rohingya Muslims from the country. India had sharply reacted to that statement.
Offering a preview of Sushma Swaraj's engagements in the US, India's Permanent Representative to the UN Syed Akbaruddin offered no indication of whether the topic of Rohingya Muslims in India would come up during the minister's meetings with world leaders.
Akbaruddin said that issues of climate change, terrorism, people-centric migration and peacekeeping are other key focus areas for India this year.
Swaraj will kick off her official engagement later today with a trilateral meeting with her American and Japanese counterparts Rex Tillerson, and Taro Kono respectively.
Aimed at lending momentum to cooperation between the three countries, the meeting also turns significant amid China flexing its muscles in the region.
In a day jam-packed with consecutive meetings, Swaraj will also participate in a high-level meeting on UN reforms, hosted by the US and chaired by President Donald Trump.
India is among the 120 countries that have supported the reform efforts of the UN Secretary General. India has said that the UN reforms need to be "broad- based and all-encompassing" and the changes should not be restricted to its Secretariat only.
Swaraj's other meetings include those with Tunisian Foreign Minister Khemaies Jhinaoui, Bhutanese Prime Minister Tshering Tobgay, Danish Foreign Minister Anders Samuelsen, Latvian Foreign Minister Edgars Rinkevics and her Bolivian counterpart Fernando Huanacuni Mamani.
Swaraj will not meet her Pakistani counterpart for a bilateral meeting, Akbaruddin had said earlier while previewing the minister's engagements.
However, the two leaders are likely to see each other during several multilateral meetings including that of SAARC and the Shanghai Cooperation Organisation (SCO).
On the topic of Pakistan-sponsored terrorism, and specifically, designating Masood Azhar a global terrorist, Akbaruddin had said that India would not rest until the Jaish-e-Mohammed chief is brought to justice.
"If I were to use a term, the matter is what we would call in judicial terms sub-judice. Currently the matter is with a UN committee. We hope that the committee will be able to fulfill its role in designating Masood Azhar who we have tried for quite some time but have not succeeded yet," Akbaruddin had said.
Among the other major highlights of this year's UN General Assembly will be US President Donald Trump's address.
This will be the first time Trump will address the UNGA and the speech he delivers on Tuesday/Wednesday will be his most high-profile yet on an international level.
The General Assembly also comes just over a fortnight after North Korea conducted its sixth, and most powerful, nuclear test.
The September 3 testing, which Pyongyang said was of a hydrogen bomb, was followed by the UN Security Council tightening its sanctions on North Korea.