A fan was arrested following the incident on Saturday, which happened after an own goal by Arsenal defender Kieran Gibbs saw United take the lead in the second half.
Manchester United substitute Darren Fletcher was involved in a heated exchange with fans behind the opposition bench moments later.
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.
“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,” a United spokesman said.
Arsenal have promised stiff action against the fan if he is found guilty.
“A male was arrested at the stadium for throwing an object towards the Manchester United bench after the first Manchester United goal,” an Arsenal spokesman said.
“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.”