Friedrich Engel (December 26, 1861 – September 29, 1941) was a German mathematician.

Engel was born in Lugau, Saxony, as the son of a Lutheran pastor. He attended the Universities of both Leipzig and Berlin, before receiving his doctorate from Leipzig in 1883. Engel studied under Felix Klein at Leipzig, and collaborated with Sophus Lie for much of his life. He worked at Leipzig, Greifswald, and Giessen. He died in Giessen. Engel was the co-author, with Sophus Lie, of the three volume work Theorie der Transformationsgruppen (tr., "Theory of transformation groups").