The terrorists were conducting a house-to-house search for the journalist, who now works in Germany, DW said Thursday.
A second relative was seriously wounded but others were able to escape, it said, without giving details of the incident.
DW director general Peter Limbourg condemned the killing, which he said showed the danger to media workers and their families in Afghanistan.
“The killing of a close relative of one of our editors by the Taliban yesterday is inconceivably tragic, and testifies to the acute danger in which all our employees and their families in Afghanistan find themselves,” he said.
“It is evident that the Taliban are already carrying out organized searches for journalists, both in Kabul and in the provinces. We are running out of time!”
The Taliban had raided the homes of at least three other DW journalists, the broadcaster said.
– THE STATESMAN