The Georgian punched referee Wolfgang Stark in the back of the head as tempers flared following the match, which was disrupted for 20 minutes due to a pitch invasion.
Stark included the incident in his match report and gave a verbal account of what had happened during a hearing into an appeal lodged by relegated Hertha into the outcome of the match.
The German Football Association (DFB) initially requested a one-year ban before its sports tribunal on Monday decided to reduce the ban to what is nevertheless a record at seven and a half months.
"While judging the ban for Levan Kobiashvili, his admission of guilt was taken into particular consideration," said the DFB's presiding judge Hans E Lorenz on the association's website.
With the suspension backdated to when the incident took place, Kobiashvili will be permitted to play again from January 1, 2013.
In addition, Kobiashvili's team-mates Thomas Kraft and Andre Mijatovic have been banned for four and three matches respectively for insulting Stark and his refereeing team. Both bans represent a one-match reduction on those initially announced last week.
An investigation is still ongoing into the conduct of Hertha midfielder Christian Lell, who is accused of spitting at opponent Assani Lukimya-Mulongoti. A decision into an initial six-game ban against Lell will be made later this week.
Fortuna won the play-off tie 4-3 on aggregate after a 2-1 victory in Berlin and a 2-2 draw at home, although the final 90 seconds of the return leg had to be played 20 minutes after a pitch invasion by buoyant home fans interrupted proceedings.
Hertha claimed that their players were scared to return to the field of play after receiving threats from some Fortuna fans as they left the pitch following the interruption, and appealed unsuccessfully against the outcome.
Fortuna player Andreas Lambertz will miss his side's first two matches back in the top flight after a 15-year absence, punished for celebrating his side's promotion by holding a flare into the air.