Anna Magdalena Godiche née Høpfner (11 January 1721 – 22 February 1781) was a Danish book printer and publisher.

Anna Magdalena was born to judge Høpfner in Haderslev.

She owned the monopoly of printing and publishing the sentences of the de facto regent Johann Friedrich Struensee and Enevold Brandt, who were famously executed in 1772.

She specialized in historical works, and printed Andreas Bussæus's Frederik 4.s Dagsregistre (1770), Niels Krag's Christian IIIs Historie (1776-79) and Historiske Efterretninger om velfortiente danske Adelsmænd (1777-79) by Tycho de Hofman.

[5] Anna Magdalena Godiche was the target of Ewald's well known epigram "Madame G."