The incident occurred after Fofana was substituted in the second half of Berlin's 1-0 loss to Napoli in the UEFA Champions League on Tuesday.
Fofana is on a season-long loan from Chelsea but has failed to score in eleven games for his new side.
Union Berlin are also on a rotten run of form, having lost each of their last nine games across all competitions, including all three Champions League group stage matches.
Fofana has apologised for his actions, writing on social media: 'Following my behaviour during my exit from the field, I wanted to apologise to the club, the coach, my teammates and the supporters.
'This gesture was not intended and in no way does it represent my attitude, all this was generated as a result of frustration because I wanted to continue helping the team to obtain a positive result.
'We will continue to work and come back even stronger in the championship and in this great competition.'
But Berlin have taken the strongest possible action against the Ivorian to deter others from taking a similar route.
"The club has decided to temporarily suspend David Fofana after Tuesday night's match," the club announced on Thursday.
"David has apologized in a personal meeting, but he will train individually for a week and return to the team next Wednesday. He will therefore not be considered for the next two games."
