Beister was sent off for a dangerous tackle on Augsburg's Daniel Baier towards the end of his side's 1-0 defeat and then received additional punishment for making insulting gestures at referee Tobias Welz as he left the field.
Hamburg have accepted the charge but were unhappy the challenge was classed as violent conduct.
"It's too severe," said coach Thorsten Fink to Germany's SID agency. "It was definitely a foul, but not violent conduct."
Beister will now be absent until May 4, meaning he will be available for just three more games this season.
It leaves Fink in a hole with fellow striker Marcus Berg also out due to a hip injury.
The Swede underwent surgery on Monday and has been ruled out for the rest of the campaign.