He was born in Großharthau in the Kingdom of Saxony the son of Prince Sizzo von Leutenberg (1860–1926) and his wife, Princess Alexandra of Anhalt (1868–1958).

On 21 April 1896, his father was recognised as a dynast of the house as Prince Sizzo of Schwarzburg, having previously lacked succession rights due to his parents' morganatic marriage.

This followed the extinction of the elder Sondershausen branch, at which point Friedrich Günther became second in line to the united principality, following Sizzo.

[2] Another interpretation of the succession to the principality of Schwarzburg in the event of the extinction of males of its Sondershausen and Rudolstadt branches was put forth by the German jurist, Hermann Schulze in 1883.

[4] He noted that inter-dynastic inheritance pacts contracted by semi-sovereign vassals of the Holy Roman Emperors remained legally enforceable in the German Empire after the abolition of the Holy Roman Empire itself in 1806, and conferred rights on male heirs superior to those of female heirs inheriting by semi-Salic primogeniture.