Born in Wernigerode, Germany, Klaproth was apprenticed as an apothecary. After working in Hannover and Danzig he moved to Berlin where he set up his own business. In 1792 he became lecturer in chemistry at the Berlin Artillery School and in 1810 he became the first professor of chemistry at the University of Berlin.

His main fame as a chemist rests on his discovery of several new elements. In 1789 he discovered zirconium, named from zircon, the mineral from which it was isolated. In the same year he extracted uranium from pitchblende and named it for the newly discovered planet, Uranus. He also rediscovered titanium in 1795, about four years after its original discovery, and discovered chromium in 1798. Klaproth used the Latin tellus (earth) in his naming of tellurium (1798), which had been discovered by the Austrian geologist Franz Joseph Muller (1740–1825) in 1782. In 1803 he discovered cerium oxide, named for the newly discovered asteroid, Ceres.