The incident occurred with 20 minutes left to play when assistant referee Christian Gittelman was hit.
Whilst Gittelman didn't suffer any serious damage, he kneeled on the pitch and began to rub the back of his head before notifying referee Benjamin Cortus that he was okay.
All the match officials left the field, and later on Gittelman was taken to hospital for an examination.
Monchengladbach were leading 2-0 thanks to second half goals from Alassane Plea and Breel Embolo.
After being made aware of the incident, the home side remonstrated with their supporters.
Moments later, the stadium announcer then said the game would be postponed because of the objects thrown onto the pitch.
Everyone vacated the pitch, and around 15 minutes later, the away side returned to applauded their supporters.
The game however would not resume and the stadium announcer then told all supporters to leave the ground.
Bochum also produced a short comment on Twitter condemning the 'stupid action' of the 'idiot fan'.
"We can only formally apologise to linesman Christian Gittelmann," the club Tweeted.
"A highly embarrassing and bitter evening for us. An extremely stupid action from an idiotic fan."
An extensive statement was then released on the club's website.
"VfL Bochum 1848 distances itself formally from those who throw cups and objects and apologises especially to the official hit for this intolerable behaviour.
"Furthermore, we naturally hope that Christian Gittelmann is doing well and that the injury does not prove to be serious.
"The focus is now on the investigation of the perpetrator, the evaluation of the images is still ongoing. VfL hopes for a quick clarification and will actively support the police in their investigations.
"Anyone who can provide relevant information for identification purposes should contact the Bochum police station.
It should have been an exciting evening of football. It has become an evening that leaves us stunned and saddened.
"The actions of individuals significantly damage the positive image that VfL Bochum 1848 and its fans have presented in recent months.
"We stand for tolerance and fair play. Throwing cups and objects is definitely not one of them."