German FA (DFB) president Reinhard Grindel has called for a clampdown after Cologne supporters verbally abused Stuttgart goalkeeper Ron-Robert Zieler.
The DFB is investigating after former Leicester City keeper Zieler was targeted by a section of the Cologne support during the second half of Stuttgart's 3-2 away win on Sunday.
Some fans, one of whom appeared to be using a megaphone, shouted sentences including: "Zieler, why don't you kill yourself?" and "Your mother is related to [former Germany keeper Robert] Enke," with the shouts clearly audible on TV.
Former Germany keeper Enke took his own life in 2009, having suffered from depression for many years.
On Monday, the DFB said it had opened an investigation, and Grindel called for action in a statement on the organisation's official website.
"Should the information be confirmed, the sports adjudication must clamp down on such scandalous language, especially in remembrance of our national team keeper, out of respect for his family and the important work of the Robert Enke Foundation," he said.
Cologne have said they will do everything they can to identify the perpetrators.
"FC Cologne distance themselves from the ugly insults against Ron-Robert Zieler and would like to make a formal apology to him and also the Enke family," a statement said.
Zieler told Express: "What can I do? Of course I hear it. The lad's only five metres behind me."