The veteran Georgia international will be unavailable for the next 12 months following his actions in the aftermath of the relegation play-off between Hertha Berlin and Dusseldorf
The tempestuous second-leg encounter on May 15 finished 2-2, with the second-tier outfit winning the tie 4-3 on aggregate to pip Hertha to a place in the Bundesliga next season.
However, shortly after the final whistle, unsavoury scenes ensued on the pitch, with match official Stark accusing Kobiashvili of punching him on the back of the head and causing him to fall down a flight of stairs.
A statement on the DFB's website indicated that Kobiashvili, who can appeal the decision, will not be eligible as of May 16 for the next 12 months.
The Georgian's team-mates Christian Lell, Thomas Kraft and Andre Mijatovic have also been dealt suspensions for their part in the fracas which followed the fixture.
Lell is now set to miss the first six games of next term for violent conduct against an opponent and for insulting the referee, while Hertha colleagues Kraft and Mijatovic will miss five and four games respectively for their involvement in the melee.
All of those involved have the right to appeal the sanctions imposed on them and request individual hearings.