1570s, "position of an ambassador," from French embassee "mission, charge, office of ambassador," Old French ambassee, from Italian ambasciata, from Old Provençal ambaisada "office of ambassador," from Gaulish *ambactos "dependant, vassal," literally "one going around" (from PIE *amb(i)-ag-to, from roots *ambhi- "around" + *ag- "to drive, draw out or forth, move").
Meaning "official residence and retinue of an ambassador" is from 1764. In earlier use were embassade (late 15c.), ambassade (early 15c.), from Old French variant ambassade.