They said the body of the drummer, 61, who lived alone at his home on the Mediterranean island of Majorca, was found by a neighbour late Sunday in a pool of blood with a injury to his neck.
Police said he appeared to have fallen from a window, and said an autopsy would be carried out to determine if the death was accidental.
The Swede played as a session musician with ABBA, which recorded and performed in 1970s and early 80s. He also toured with the group.
Brunkert retired to Majorca, where he performed with his jazz group.
ABBA’s four stars Björn Ulvaeus, Benny Andersson, Agnetha Fältskog and Anni-Frid Lyngstad became international sensations with hits such as “Money, Money, Money,” “Waterloo,” “Fernando” and “Dancing Queen.”
Despite having broken up a quarter of a century ago, the group still sells between two and three million albums a year.