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By law, "the Sundays and the public holidays remain protected as days of rest from work and of spiritual elevation" (Art. 139 WRV, part of the German constitution via Art. 140 GG). Thus all Sundays are, in a manner, public holidays – but usually not understood by the term "holiday" (except for, normally, Easter Sunday and Pentecost Sunday).
Public holidays apart from the Sundays (there must be some of them constitutionally) can be declared by law by either the Federation or the Länder for their respective jurisdictions. By federal law, only the German Unity Day is made a holiday at present (Unity Treaty, Art. 2 sect. 2); the others, even the ones celebrated all over Germany, are made holidays by state legislation.