Schütz was born to a town clerk and his second wife. Christoph Schütz worked in the administration at Gera, but later took over an inn after his own father died. Heinrich was the second of eight children, and the eldest son. He maintained a close relationship with his family, especially his brother Georg.
In 1590, the Schütz family moved to Weissenfels, where Schütz began music training with a local organist. Several years later, the Landgrave Moritz of Hessen-Kassel heard the boy sing, and acquired him for the court at Kassel.
There, the young Schütz was installed as a choirboy, and his education began in earnest. He excelled in all subjects, and showed an aptitude for languages. He learned Latin, Greek, and French. Apparently, composition was not a major part of his education, though he did take classes in counterpoint. Schütz then went on to study law at the University of Marburg under the pressure of his parents.
While at the university, Schütz recieved correspondence from the landgrave, notifying him that the Venetian master Giovanni Gabrieli "was still alive, [and] I should not miss the chance to hear him and learn something from him". The landgrave granted Schütz a two year stipend to travel to Italy and study. He started off shakily, since he did not have a strong background in music, but he eventually got a steady footing academically. Towards the end of the two year grant, Gabrieli decided that Schütz should stay and continue his studies. He remained in Venice for almost four years, until Gabrieli's death in 1612.
It was during this time in Venice that Schütz published his first collection of music, Il primo libro de madrigali. This book of five-voice madrigals was dedicated to the Landgrave Moritz and is dated May 1, 1611. This first compositional effort won Schütz praise from the Venetian intelligencia.
After his return to Kassel, Schütz continued his employment at Moritz's court as second organist. In 1614, Elector Johann Georg I of Saxony heard Schütz play the organ, and in 1615 requested that Moritz "lend" him the services of the musician for two years. After a disagreement, the landgrave was forced to acquiesce. Schütz left for the elector's Dresden court in August of 1615.