Modi, who will also hold talks with US President Barack Obama in a previously announced US visit, will first stop in Afghanistan to jointly inaugurate a dam with President Ashraf Ghani on Saturday.
He then travels to Qatar and Switzerland before arriving in Washington on June 6 for a three-day visit that will see him address a joint meeting of the US Congress on June 8.
Narendra Modi to visit Afghanistan to open dam
"These will be the first visits for Prime Minister Modi to Qatar, Switzerland and Mexico," foreign ministry spokesperson Vikas Swarup told AFP.
Modi will reach Qatar on Saturday evening and meet with the Emir of Qatar, business leaders and members of the Indian expat community on Sunday.
Besides vital security and energy interests - India gets almost two thirds of its crude oil from the Middle East - Modi will be eyeing investments from Qatar's sovereign wealth fund for key infrastructure projects.
Modi will meet the President of the Swiss Confederation on Monday before going on to Washington.
In Switzerland, which is India's fifth-largest trading partner, a Modi-led delegation will work for closer ties with the country's renewable energy and vocational education sectors.
The Indian prime minister will reach Mexico late Wednesday for a meeting with President Enrique Peña Nieto before flying back to New Delhi the same day.
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