He said that Erdogan's strident style "had apparently led some to feel motivated to try to threaten and harass my wife," in comments broadcast Tuesday by news channel NTV.
"Of course, this is a terrible outcome," he said without giving further details, at a time when relations between the NATO allies have plunged to their lowest point in years.
On Saturday, Erdogan launched a bitter personal attack on Gabriel, who has frequently criticised the president's leadership and his treatment of opponents and critics.
Relations between Turkey and Germany, home to three million ethnic Turks, have deteriorated sharply, particularly since a failed coup against Erdogan over a year ago and a subsequent mass crackdown on its alleged plotters.
Among the alleged state enemies and terrorist supporters behind bars in Turkey are several German or dual Turkish- German citizens, including journalists and rights workers.
Erdogan has charged that Germany is sheltering Kurdish militants, coup plotters and terrorists.
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