United boss Jose Mourinho is understood to have taken exception to what he deemed to be excessive celebrations from City's players in the wake of their 2-1 victory at Old Trafford as the league leaders moved 11 points clear at the top of the table.
A heated exchange followed with City goalkeeper Ederson, and the row eventually spilled out to involve numerous players and staff from both clubs.
Mourinho allegedly had milk and water thrown at him during the melee, while Arteta suffered a cut to the head and was left with blood running down his face as a result of the skirmish.
No punches are thought to have been thrown by either side, but reports have claimed that Mourinho was hit on the head by an empty plastic bottle - although the United boss conducted his post-match press conference with no mention of the incident.
City's win was their 14th Premier League victory on the bounce, setting a new single-season record for the competition.