A fan was arrested following the incident which happened after an own goal by Kieran Gibbs saw United take the lead in the 2-1 win on Saturday
Arsenal have promised stiff action against the fan if he is found guilty.
United confirmed an incident, understood to involve red wine, took place but are happy with how Arsenal dealt with the situation and will not be making a complaint.
A United spokesman told Press Association Sport: "There was an incident after the first goal but Arsenal's staff and stewards acted quickly and professionally to it
Contrary to reports in today's media, we will not be making a complaint to the FA."
Manchester United substitute Darren Fletcher was involved in a heated exchange with fans behind the opposition bench following the incident.
An Arsenal spokesman said: "A male was arrested at the stadium for throwing an object towards the Manchester United bench after the first Manchester United goal.
''There will be full co-operation between Arsenal and the Met Police - we do not tolerate anti-social behaviour
If found guilty, the individual will also be banned by club.''
Former United manager Sir Alex Ferguson had previously complained about the visitors' dug-out at the Emirates being "too open" and not providing adequate protection for his players and staff.
Source : PA
Source: PA