Around 7pm on Sunday February 16, a large number of under-18s were involved in anti-social behaviour at the fast food restaurant on Bessingby Industrial Estate.
This resulted in staff being subjected to abuse, damage caused and police attendance.
A male and female juvenile were detained and police say they will be taking formal action in relation to their behaviour and damage caused.
A spokesperson from Humberside Police said: "We would like to re-assure members of the public present, who may have witnessed the incident, that this type of behaviour will NOT be tolerated and positive action will be taken.
"Please can we seek the support from parents to ask their children whether they were present at McDonald's during the evening of this incident and if so to provide them education about the consequences of being involved in such anti-social behaviour.
"The Police work closely with the East Riding of Yorkshire Council to combat anti-social behaviour and will take positive action against any individual identified as responsible."