Johan Peter Weisse (13 August 1832 – 7 March 1886) was a Norwegian philologist.
He was born in Fluberg as a son of physician Joachim Frederik Weisse and his wife Grethe Fleischer. His grandfather had migrated to Norway from Brandenburg. The family moved to Trondhjem in 1833.
He married his own cousin Maja Stang (1843–1916) in July 1863 in Fredrikshald. She was an aunt of engineer Olaf Stang, and a third cousin of engineer Theodor Stang and politician Emil Stang. In May 1893 one of their daughters married politician Gabriel Gabrielsen Holtsmark. Through them, Weisse was the maternal grandfather of professor Johan Peter Holtsmark, professor Anne Holtsmark and painter Karen Holtsmark.
He took his examen artium at Trondhjem Cathedral School in 1850. He read languages such as Norse, Anglo-Saxon, Gothic, Old Danish, Old Swedish, Greek, Latin, Russian and Cuneiform script already at that time, as witnessed by his diary Litterær Dagbog. He started studying philology in 1851. From 1853 to 1855 he had to stay in Rome because of health issues, but he studied the city vividly. He was a part of a Nordic intellectual group here, which included Julius Middelthun, Christoffer Borch, Georg Forchhammer and Niels Ravnkilde. He finally graduated from the Royal Frederick University with the cand.philol. degree in 1858.