It comes after the Ivorian refused to shake hands with head coach Urs Fischer after being substituted in the 70th minute of Union's 1-0 Champions League defeat to Napoli on Tuesday.
After making his way to the touchline, Fofana snubbed his manager before taking his place on the bench. The 20-year-old was later seen in tears by television cameras.
Fofana was quick to acknowledge his actions by issuing an apology to Fischer, his teammates and the club's supporters via his Instagram account.
He said: "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.
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"We will continue to work and come back even stronger in the championship and in this great competition."
Fischer told reporters at full time the reasoning behind the decision to haul the Ivorian off claiming he wanted to keep his attack fresh.
Fofana is yet to find the target for his new club after signing on loan during the summer.
He has clocked up 11 appearances for the Bundesliga side adding to his four appearances for Chelsea following his move from Norwegian side Molde in December 2022.