The video, obtained by The Sun shows the players in a London club days before the start of the season appearing to use nitrous oxide, and while the gas is freely available it is illegal to sell for recreational purposes.
Arsenal players will be "spoken to" by club chiefs after images emerged allegedly showing four members of the first team inhaling nitrous oxide.
After seeing the video, an Arsenal spokesperson told BBC Sport that players would be "spoken to and reminded of their responsibilities".
The incident is reported to have taken place in August, before the start of Arsenal's season.
Some of the players reportedly collapsed and passed out after inhaling the gas.
Players including Mesut Ozil, Pierre-Emerick Aubameyang, Alexandre Lacazette and Matteo Guendouzi feature in the footage, which appears to come from CCTV footage and was published by The Sun newspaper on Friday.
The use of nitrous oxide in balloons has becoming increasing popular at parties.
"What I'm struggling to work out about Arsenal's fantastic run is why Pierre-Emerick Aubameyang's on-field brilliance is not being highlighted more".
The Gunners are now on an unbeaten run of 20 straight matches following their 2-2 draw with Manchester United midweek.