Heinrich Bach (16 September 1615 – 10 July 1692) was a German organist, composer and a member of the Bach family.
Heinrich Bach was born at Wechmar, Germany, and is the father of the so-called Arnstädt Line. After the early death of his father, his older brother Johannes Bach continued his music education and teaching him organ playing. They moved to Suhl (Stadtpfeifer Hoffmann) and Schweinfurt. From 1635 to 1641, he was Ratsmusikant in Erfurt Ratsmusikanten-Compagnie led by Johannes. From 1641, he became organist in Arnstadt St. Mary's Church and the Upper Church, a post he kept until his death. In 1642, he married Eva Hoffmann, the younger daughter of Suhl Stadtpfeiffer Hoffmann. He died in ,Arnstadt.
Three of his sons, Johann Christoph Bach, Johann Michael Bach and Johann Günther Bach, were musicians.
Only a few of his works have been preserved: