Man City have now lost two consecutive games in the Premier League.
Manchester United lost 3-1 at Arsenal in the Premier League on Sunday,
Harry Maguire was earlier close to leaving Manchester United.
Manchester City are eyeing a third straight Premier League title.
Arsenal are currently second in the 2022-23 Premier League table.
There are contradicting reports about who started the altercation.
Treble-chasing City, on top for the first time in 10 weeks, have won their past eight league games and are unbeaten in their last 18 matches in all competitions.
Second placed City are now just two points behind Arsenal with two games in hand.
The Arsenal women squad was flying back to London from a Champions League match in Germany when the incident occurred.
Showing any weakness against Pep Guardiola's men in a title race is likely to prove fatal.
Manchester City have qualified for the semi-finals of the 2022-23 Champions League.
Arsenal are four points clear at the top of the 2022-23 Premier League table.
Liverpool are currently eighth in the 2022-23 Premier League table.
The assistant referee is accused of throwing an elbow after the Scotland international approached him.
In the clash between the two sides that have dominated English football over the past five years, City were a class apart despite the absence of Erling Haaland due to injury.
Few would have expected Arsenal to be so close to glory after they blew their attempt to finish in the top four last season.
The Gunners are leading the race to clinch the Premier League title this season.
Arsenal lost to Sporting Lisbon 3-5 on penalties (3-3 agg) on Thursday night.
Arsenal are five points clear at the top of the 2022-23 Premier League table.
Arsenal manager Mikel Arteta said the result was "a huge blow" and blasted his side for wasting chances.
It was Arsenal's 11th victory from 14 away league matches this season
Arsenal's unbeaten home record came to end on Wednesday as City stormed the Emirates 3-1.