The video, which was first published by US celebrity website TMZ, showed Beyonce’s sister lashing out in a lift after the Met Gala on 5 May.
A security guard intervened in the apparent altercation. There is no audio on the recording.
The Standard Hotel said it was “shocked and disappointed” by the leak and had identified the person responsible.
The employee was fired for “breaching the security policies of the hotel and recording the confidential CCTV video”.
The hotel added that it would hand over “all available information to criminal authorities”.
Representatives for Jay Z, Beyonce and Solange have made no comment on the video.