Solange "Attacks" Jay-Z Inside An Elevator, Kicking & Swinging! - Video Inside

Jay Z was ferociously assaulted by Beyonce's sister Solange  ... who was wildly kicking and swinging at him inside an elevator ... and the attack was captured on surveillance video.

According to our sources, it all went down at a Met Gala after party last week at theStandard Hotel in NYC.  In the video ... Jay Z, Beyonce and Solange step into the elevator ... and then Solange goes crazy, screaming at Jay before unleashing a violent attack. 

A large man -- who appears to be a bodyguard -- attempts to hold Solange back, but she manages to connect at least 3 times.  At one point Solange throws a kick and Jay grabs her foot, but never attempts to strike her.  Beyonce stands by without getting physically involved. 

It's unclear what triggered the fight.

And this is interesting.  When you look closely, you see the bodyguard hit the emergency stop switch on the 12th floor -- mid fight -- presumably to keep the fight private.

This photo was taken as they left the party ... and Solange looks pissed!