Roger Federer Swarmed By Massive Crowd of Fans in NYC

Roger Federer caused insane pandemonium out in the Big Apple on Tuesday ... when a crush of passionate fans crowded together to try to get a brief glimpse of the tennis superstar.

TMZ Sports got video of the insane scene outside Uniqlo on Fifth Avenue in NYC ... where Federer was doing a Q&A for the clothing brand.

Of course ... Federer -- currently the #3 ranked male tennis player -- famously left Nike for the Japanese company last year for $300 MILLION.

Just by looking at the scene outside the store, it's clear 38-year-old Federer is still one of the biggest sports superstars on the planet.

Of course, it's something that tends to happen when international ballers hit up NYC ... remember how bonkers it got when Manchester United superstar Paul Pogba hit up the Adidas store last month?