The Netherlands international was sent off with five minutes remaining of their 1-0 victory following a rash challenge on Manuel Schmiedebach.
A straight red card would normally only incur a three-game ban, however Huntelaar's suspension has been extended after confronting referee Sascha Stegemann after being dismissed, but the Gelsenkirchen side have said they will look to get the ban reduced.
"Contrary to the Supervisory Committee’s assumptions, we believe this was not a matter of violent conduct," general manager Horst Heldt told the club's official website.
"That’s not something Klaas-Jan would do. Surely, the red card was justified, but we consider a six-match-ban too high a punishment. This is why we are appealing."
Roberto Di Matteo must now do without Huntelaar's services for crucial league matches with Bayern Munich, Borussia Monchengladbach and Borussia Dortmund.
If an appeal is unsuccessful, Huntelaar will be able to feature in their Champions League last-16 tie with Real Madrid, but will not play another league game until mid-March.
"After re-watching the incident, I have to admit the referee was right," Huntelaar told the club website.
"[But] it was definitely not my intention to be derogatory towards the referee. If people see it like that, then I am sorry and would like to apologise to him."
