Heinrich Simrock was the brother of the music publisher Nikolaus Simrock, whose firm still exists today. He was born in Bonn in 1754 and, like his brother, learned to play the horn. He is believed to have given, together with Nikolaus, the first performance of Beethoven's Sextet Op. 81b, which was later published by Nikolaus Simrock's firm. In the late 18th century, Heinrich Simrock moved to France.
In Paris he later worked as a horn player and teacher at the Conservatoire. He also represented his brother's publishing house in France. From 1802 he owned a music shop in Paris and was among those who helped introduce Beethoven's music to France.