Anthony Günther married Sophie Catherine (28 June 1617 – 22 November 1696), a daughter of Alexander, Duke of Schleswig-Holstein-Sonderburg and Dorothea of Schwarzburg-Sondershausen.

[citation needed] S. Baring-Gould relates the following interesting anecdote about the count in his book "Strange Survivals Some Chapters in the History of Man": In 1615 Count Anthony Günther of Oldenburg, on visiting a dyke in process of construction, found the workmen about to bury an infant under it.

The count interfered, saved the child, reprimanded the dam-builders, and imprisoned the mother who had sold her babe for the purpose.

Singularly enough, this same count is declared by tradition to have buried a living child in the foundations of his castle at Oldenburg.

[1] The Haus "Graf Anton Günther" is a historic house in central Oldenburg, dating from 1682.