He was the fifth of the six children born to Georg Albrecht of Brandenburg-Bayreuth-Kulmbach by his first wife, Princess Marie Elisabeth of Schleswig-Holstein-Sonderburg-Glücksburg.
His younger brother - and with him, the two only children of his parents who survived to adulthood - Karl August, died unmarried and childless in 1731 aged sixty-eight.
In 1694 he accepted the invitation of his kinsman, the Margrave of Brandenburg-Ansbach, to move in with his family in the Castle Schönberg, Ansbach enclave in the Imperial City (German: Reichsstadt) of Nuremberg.
Under the terms of this treaty, he renounced his succession rights over the Franconian estates of the House of Hohenzollern (the principalities of Ansbach and Bayreuth) in favour of Prussia.
After Christian Heinrich's death, his oldest son Georg Frederick Karl pursued the abolition of the Contract of Schönberg; only in 1722, after long and difficult discussions, did he finally recover the succession rights of his family to Bayreuth and Ansbach.