Punia, who won the 65kg men's freestyle gold at the recent Asian championships, will be among top wrestlers selected by the American governing body for the May 6 tournament.
The 25-year-old will take on two-time US national champion Yianni Diakomahlis in the "Grapple at the Garden" Beat the Streets event which since 2010 has become a major showcase for international wrestling.
"If you see it from a player's perspective then it is quite an experience fighting at Madison Square Garden. It's great exposure. But there is happiness and there is fear," Punia told AFP.
"Happiness because I am the first Indian to be invited there. Fear because of my country's expectations whether I will be able to meet up with it or not," added Punia, who hails from Jhajjar district of the north Indian state of Haryana.
Punia has eight gold medals from his previous nine international tournaments including last year's Commonwealth and Asian Games.
Punia's mentor Yogeshwar Dutt who won the 60kg bronze at the 2012 London Olympics praised his achievement.
"He has been winning all this time and he will triumph at Madison Square Garden," Dutt told AFP.
"He wins finals everywhere he goes. I just tell him to keep working hard."
American wrestler Kyle Snyder, who won the 97kg title at the 2016 Olympics in Rio, and Jordan Burroughs — 2012 London Olympics gold winner — are the other top attractions at the event.
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