Born at Oberscheden, near Göttingen, the son of a blacksmith, he studied composition. He joined the Dresden town band in 1716, studied counterpoint in Vienna under Jan Dismas Zelenka the following year, and in 1718 was appointed oboist in the Polish chapel of Augustus II; he also continued to play in Dresden.
Finding little opportunity for advancement as an oboist, he took up the flute, studying for four months with P. G. Buffardin. Quantz traveled to Italy in 1724, to study counterpoint in Rome with Gasparini ; he also journeyed to Paris (1726-27), where he added a second key to his flutes to help with intonation (playing in tune), and to England in 1727, where he met Handel.
Upon his return to Dresden he was made a member of the court Kapelle. From 1728 he instructed Prince Frederick on the flute, and moved to Berlin in 1741 after Frederick (the Great) became King of Prussia.
He was the most famous and expert flautist of his day. In Berlin, Quantz was exempt from playing in the opera orchestra; instead, his duties revolved around the king's private evening concerts, where the repertoire (at least in later years) consisted primarily of works by Quantz and Frederick himself.
His compositions include over 200 flute sonatas and 300 flute concertos, in addition to trio sonatas and some vocal music; few of his works were published after he moved to Berlin. He died in Potsdam.
Quantz is best known for his treatise Versuch einer Anweisung die Flöte traversiere zu spielen (1752), an exhaustive work that discusses nearly all aspects of performance, from ornamentation and accompaniment to criteria for evaluating compositions and musicians.
Quantz also was a skilled flute maker; examples of his instruments can be found in Berlin and Washington, D.C.