Johann Gottfried Müthel (January 17, 1728 – July 14, 1788) was a German composer and noted keyboard virtuoso. Along with C.P.E. Bach, he represented the Sturm und Drang style of composition.
As far as is known, he was the first to use the term fortepiano in a published work, in the title of his Duetto für 2 Clavier, 2 Flügel, oder 2 Fortepiano (1771), which reflects the rising popularity of the instrument at that time.
He was born in Mölln in the Duchy of Lauenburg, the fifth of nine children. His father was Christian Caspar, an organist and friend of Georg Philipp Telemann. He studied music with his father, and later Johann Paul Kunzen in Lübeck. When only 19 years of age, he became a court organist and harpsichordist for Duke Christian Ludwig II of Mecklenburg-Schwerin, in Schwerin.
In 1750 he was given leave to become the student of Bach in Leipzig. He became Bach's last pupil, beginning study only three months before the master's death. In that time, he notated a number of the blind composer's final works, including parts of the Orgelbüchlein. According to Bach's biographer Philipp Spitta, he was present at Bach's deathbed, and took over his duties for nine weeks.
Subsequently Müthel took lessons from Johann Christoph Altnickol, who had also been living and studying with Bach. Afterwards he spent a good deal of time on travel, and he met other composers, the most notable of whom was C.P.E. Bach (then residing at the court of Frederick II of Prussia at Potsdam), with whom he maintained a lifelong friendship and correspondence.