In 1590 the family moved to Weißenfels, where his father managed the inn "Zum güldenen Ring". His father eventually served as burgomaster in Weißenfels, and in 1615 purchased another inn known as both "Zur güldenen Sackpfeife" and "Zum güldenen Esel" – which he renamed "Zum Schützen".

While Schütz was living with his parents, his musical talents were discovered by Landgrave Moritz von Hessen-Kassel in 1598 during an overnight stay in Christoph Schütz's inn. Upon hearing young Heinrich sing, the landgrave requested that his parents allow the boy to be sent to his noble court for further education and instruction. His parents initially resisted the offer, but after much correspondence they eventually took Heinrich to the landgrave’s seat at Kassel in August 1599.

After being a choir-boy he went on to study law at Marburg before going to Venice from 1609–1612 to study music with Giovanni Gabrieli. Gabrieli is the only person Schütz ever referred to as being his Teacher. He also inherited a ring from Gabrieli shortly before the latter's death. He subsequently was organist at Kassel from 1613 to 1615.

Schütz moved to Dresden in 1615 to work as court Composer to the Elector of Saxony. His Dresden compositions after the Thirty Years' War were more lightly orchestrated than those before. In 1619 Schütz married Magdalena Wildeck who had been born in 1601. She bore two daughters before her death in 1625: Anna Justina born in 1621 and Euphrosyne born in 1623.

In Dresden Schütz sowed the seeds of what is now the Sächsische Staatskapelle Dresden, but left there on several occasions; in 1628 he went to Venice again, where he met and studied with Claudio Monteverdi. In 1633 he was invited to Copenhagen to compose the music for wedding festivities there, eventually returning to Dresden in 1635. He again conducted an extended visit to Denmark in 1641. The Thirty Years' War ended in 1648, and he became more active. In 1655, the year that his daughter Euphrosyne died, he accepted an ex officio post as Kapellmeister at Wolfenbüttel.

Schutz did not put on large-scale compositions until the 1660s, when he composed the greatest Passionmusic before Bach.

Schütz died in Dresden from a stroke in 1672 at the age of 87. He was buried in the old Dresden Frauenkirche, but his tomb was destroyed in 1727 when the church was torn down to build the new Dresden Frauenkirche.

Schütz's compositions show the influence of his Teacher Gabrieli (displayed most notably with Schütz's use of resplendent polychoral and concertato styles) and of Monteverdi. Additionally, the influence of the Netherlandish composers of the 16th century is prominent in his work. His best known works are in the field of sacred music, ranging from solo voice with instrumental accompaniment to a cappella choral music. Representative works include his Psalmen Davids (Psalms of David, Opus 2), Cantiones sacrae (Opus 4), three books of Symphoniae sacrae, Die sieben Worte Jesu Christi am Kreuz (Seven words of Jesus Christ on the Cross), three Passion settings and the Christmas Story. Schütz's music, while starting off in the most progressive styles early in his career, eventually grew into a style that is simple and almost austere, culminating with his late Passion settings. Practical considerations were certainly responsible for part of this change: the Thirty Years' War had devastated the musical infrastructure of Germany, and it was no longer practical or even possible to put on the gigantic works in the Venetian style which marked his earlier period.