Interior Minister Thomas de Maiziere said that by supporting Hamas, the donor group -- the IHH (Internationale Humanitaere Hilfsorganisation) -- had violated a clause in the German constitution on international goodwill.
The IHH called the ban a "disgrace" and said it would take immediate legal action against it.
Hamas, which controls Gaza, refuses to recognize Israel.
Germany has staunchly supported Israel following the “Nazi genocide” of European Jews in World War Two and has strongly criticized Hamas, which Israel considers to be a terrorist organization.
De Maiziere said the Frankfurt-based IHH abused donors' good intentions "to support a terrorist organization with money supposedly donated for charitable purposes."
"Organizations that directly or indirectly align themselves from German soil against Israel's very right to existence have forfeited their right to form an association," de Maiziere added in a statement.
IHH chairman Mustafa Yoldas said the ban was "misanthropic" and denied humanitarian aid to the people of Gaza.
"It's macabre that the interior minister is punishing those looking after orphaned children instead of criticising the ones turning children into orphans," he said in a statement.
"We're firmly convinced these measures will not stand up to any court in a country under the rule of law," he added.