City midfielder Nasri, who did not feature in the match due to suspension, and Chamakh, who is currently on loan at West Ham from Arsenal, are seen walking together towards the Emirates Stadium.
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Several Arsenal supporters appear to insult Nasri and Chamakh before one fan approaches and confronts the France international.
Arsenal said they were aware of the video but had no statements to make when contacted by Goal.com on Monday morning, while Manchester City were unavailable for comment.
At the beginning of the video, a man out of shot is heard to shout "there's that w***** Nasri" before both players are abused.
A fan extends his hand to Nasri, before withdrawing it, prompting the Frenchman to respond: "What the f*** is wrong with you?"
After further insults aimed at both players, Chamakh rounds on the supporters, saying: "Show a bit of respect," which is met with further taunting and goading.
Nasri left the Gunners for Manchester City in a £24 million deal in the summer of 2011, after refusing to sign a new contract at the Emirates Stadium.