He was the fifth of the six children born to Georg Albrecht of Brandenburg-Bayreuth-Kulmbach by his first wife, Marie Elisabeth of Schleswig-Holstein-Sonderburg-Glücksburg.
From his father's second marriage with Sophie Marie of Solms-Baruth-Wildenfels, Christian Heinrich had a half-brother, Georg Albrecht, who was born three months after the death of his father in 1666.