Asamoah was born in Ghana but grew up in Germany
The German Football Federation (DFB) has fined Hansa Rostock U$25,000 for the racist abuse suffered by Ghana-born striker Gerald Asamoah.
Racist chants were aimed at the Schalke player, who featured for Germany at the World Cup, during Saturday's German Cup game.
The DFB's sport court also ordered the third division east German club to play their next home match without any spectators because of the incidents in the match.
"The reason for the punishment is the continued racist shouts aimed at Schalke's international player Gerald Asamoah," DFB spokesman Harald Stenger said in a statement.
The DFB said that Hansa Rostock accepted the ruling.
It is the first punishment meted out by the DFB following new disciplinary regulations aimed at clamping down on racism in the game.
In June, Fifa warned it will suspend national associations who fail to impose the new tough rules that came into force in July.
Meanwhile, Rostock manager Stefan Studer has given Asamoah a personal apology.
"This is simply shameful and disgusting," Schalke manager Mirko Slomka said.
"Rostock has a national team game soon - maybe something can be done there."
Rostock hosts Germany's friendly against Georgia on 7 October.
Asamoah was among players targeted by right wing groups heading into the World Cup.