Footage from the Emirates Stadium showed Keane's Sky Sports co-pundit Micah Richards appearing to hold back an unidentified man, who is believed to have aimed a headbutt at Keane.
The United legend can also be seen gesturing towards the man in a video that has been widely circulated on social media.
The incident took place late on in the game when Alejandro Garnacho's goal was ruled out for offside.
Keane and Richards were believed to be making their way down to the side of the pitch for their post-match presenting duties before the confrontation took place.
The Metropolitan Police have now said: "Police are investigating an incident at Emirates Stadium on Sunday, 3 September, during which a man was assaulted.
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"On Monday, 4 September, a 42-year-old man was arrested on suspicion of assault [ABH].
"The man has been taken into police custody. Enquiries are ongoing."
Both Keane and Richards have provided the Metropolitan Police with statements of the incident.
Arsenal emerged as the victors in a dramatic finish in north London despite Marcus Rashford giving United the lead.
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Martin Odegaard hit back for the Gunners a minute later and Garnacho thought he had won it late on.
However, the goal was ruled out, with Declan Rice and Gabriel Jesus scoring in stoppage time to seal the win.