Friedrich Wilhelm Grützmacher (1 March 1832 – 23 February 1903) was a noted German cellist in the second half of the 19th century.
Grützmacher was born in Dessau, Anhalt, and was first taught by his father. Soon he began studying cello with Dotzauer's pupil, Karl Dreschler (1800-1873).
In 1848 he was discovered in Leipzig by the famous violinist, Ferdinand David, who arranged some concerts for him. In 1850 he became solo cellist in the Leipzig theatre orchestra, the Gewandhaus Concerts, and professor at the Leipzig Conservatory. He played in the David String Quartet.
In 1860 Grützmacher moved to Dresden to be principal cellist of the Court Orchestra, and head of the Dresden Musical Society. In 1877 he became a professor at the Dresden Conservatory. He concertized all over Europe and Imperial Russia, where he became a friend of the famous cellist Karl Davidov. He played the first performance of Richard Strauss's Don Quixote in Cologne in 1898. He was the teacher of Wilhelm Fitzenhagen (of thumb position fame), and Hugo Becker (whose etudes are still used).
Grützmacher is most famous today for taking samples of four different works to form his edition of Luigi Boccherini's Concerto in B flat, still being published and performed. He is also known for rearranging J.S. Bach's Cello Suites with additional chords, passages and embellishments. His cadenzas for the cello concertos by Boccherini and Joseph Haydn are often performed to this day.