Deputy Minister for Youth Karina Bolanos lost her job after a video showed her lying in bed, pointing at her breasts and inviting a man she refers to as "little one" to join her.
Bolanos told cable TV network CNN en Espanol the video was made years ago and was put onto the Internet by a computer engineer who stole it and was trying to extort her.
The clip was uploaded to YouTube over the weekend, and quickly went viral.
Costa Rica's Ministry of Culture and Youth said in a statement the video and related legal issues made her position untenable.
The incident is an embarrassment to President Laura Chinchilla, whose Cabinet has suffered a string of resignations since she took power two years ago.
Local media said she declined to comment on the Bolanos scandal.
"I will not address the issue. Any more questions?", newspaper La Nacion reported her saying after a public event.
