As a young physician he studied with Franciscus Cornelis Donders in Utrecht, William Bowman in London, Albrecht von Graefe in Berlin and Hermann von Helmholtz in Heidelberg.

In 1869 he founded the New York Ophthalmic and Aural Institute, which from 1913 to 1939 was called the Herman Knapp Memorial Hospital.

In 1869, with Salomon Moos (1831–1895), he founded the "Archives of Ophthalmology and Otology" (Archiv für Augen- und Ohrenheilkunde), an international scientific monthly journal that was published in Wiesbaden (in German) and New York (in English).

He devised his own version of an ophthalmotrope, a device used in physiological optics to demonstrate the action of ocular muscles individually or in various combinations.

Several instruments used in eye surgery bear his name, including the "Knapp trachoma forceps".