Knudtzon was born in Trondheim in Sør-Trøndelag; he was the sixth and youngest child of Hans Carl Knudtzon (1751–1823), a merchant and burgomaster, and Karen Knudtzon (née Müller, 1752–1818).
Knudtzon was born in Bredstedt, North Frisia (now part of the Schleswig-Holstein state in Germany), the son of Nicolai Knudtzen (1698–1785), merchant, and his wife, Magdalena (1726–1803), née Clausen.
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