Footage circulating on social media shows Sky Sports pundits Micah Richards and Keane involved in an altercation with an individual.
It is understood the former Man Utd captain was the alleged victim of a headbutt, which was not shown in the video.
Sky confirmed Richards, a former Man City and England international, was "acting to defuse a situation."
In a statement Sky said: "We understand the police are investigating an alleged assault by a member of the public immediately preceding the footage circulating on social media. In the footage seen, Micah Richards was acting to defuse a situation."
A Metropolitan police read: "Police are investigating following an assault that is alleged to have occurred at the Emirates Stadium during an Arsenal v Manchester United match on Sunday, 3 September.
"There have been no arrests. Inquiries are ongoing. Any witnesses or those with information are asked to call 101 ref CAD 6961/3 Sept."