A Cardassian embassy was any one of several permanent diplomatic missions to other governments which represented the Cardassian Union and its interests.
Elim Garak was once assigned to the Cardassian embassy on Romulus, as a gardener. This was, however, a cover for his work with the Obsidian Order. During this time, he may have been involved in several assassinations, including that of Proconsul Merrok and Sub-Commander Ustard. (DS9: "Broken Link")
In 2372, Dukat expressed a desire to send Gul Marratt to the embassy on Breen, a planet known for its cold. He wished to do so because of Marratt's romantic relationship with Dukat's wife, who had left him after discovering the existence of Tora Ziyal. (DS9: "Return to Grace")