The Standard Hotel issued a statement saying it is "shocked and disappointed that there was a clear breach of our security system".
US celebrity website TMZ posted the minute-long video on Monday and said it was shot last week inside a Standard Hotel elevator.
It appears to show Solange attacking Jay Z in his wife Beyonce's presence. A security guard intervenes. There is no audio.
The hotel says the leaked video violates the confidentiality it provides customers.
"We are investigating with the utmost urgency the circumstances surrounding the situation and, as is our customary practice, will discipline and prosecute the individuals involved to our fullest capacity."
TMZ posted a longer, three-minute version of the video later. Representatives for Beyonce, Jay Z and Solange declined to comment.
The footage shows the performers in the outfits they wore to the Met Gala last week.
Jay Z, 44, and Beyonce, 32, were married in 2008. They will kick-off their co-headlining On The Run Tour on June 25 in Miami.
Solange, 27, recently performed at the Coachella Valley Music and Arts Festival, where Beyonce joined her onstage.