The Standard Hotel said the person had been sacked for "breaching the security policies of the hotel and recording the confidential CCTV video".
Celebrity website TMZ posted the three-minute video on Monday and said it was shot last week inside a Standard Hotel lift.
The video appears to show Solange attacking Jay Z in Beyonce's presence. A security guard intervenes. The footage shows the performers in the outfits they wore to the Met Gala last week. There is no audio.
The hotel said after the video was first aired that it was "shocked and disappointed" by the security breach. It said yesterday that it will turn over "all available information to criminal authorities".
Jay Z and Beyonce, who were married in 2008, will kick off their co-headlining On The Run Tour on June 25 in Miami.
Solange recently performed at the Coachella Valley Music and Arts Festival, where Beyonce joined her onstage.