The Glaswegian act - whose hits include Geraldine and Daddy's Gone - said they were "sad" at her departure.
McKay was noted for her unusual playing style, standing rather than sitting as she performed.
Glasvegas are currently in Los Angeles writing the follow-up to their self-titled debut album. They are due to start recording in the summer.
Singer James Allan said: "We are really sad that Caroline has decided to leave as she is one of the coolest drummers around, but we respect her decision and say goodbye with all our love and luck."
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