Bacardi, which owns the eponymous rum brand as well as Grey Goose vodka, Dewar’s whisky and Martini vermouth, said a replacement would be announced in due course.
Ed Shirley, president and chief executive officer of Bacardi Limited, said: "We thank Silvia for her contributions and dedication to the Company and wish her every success."
The news of her departure comes in the middle of global ad reviews for Dewar’s and Bacardi.
Lagnado joined Bacardi in 2010, having worked at Unilever for 24 years.
She worked on the Dove toiletry brand, including campaigns such as "Campaign for Real Beauty", but was most recently executive vice-president for savoury products at the FMCG giant.
At Bacardi Lagnado replaced Stella David, who stepped down from the role of chief marketing officer in August 2009. David had spent 15 years at Bacardi and left to join William Grant & Sons as chief executive.