Ludvig is a Scandinavian variant of the German name Ludwig. People with the name include:

• Ludvig Åberg, Swedish professional golfer

• Ludvig Almqvist, Swedish politician

• Ludvig Aubert, Norwegian Minister of Justice

• Ludvig Bødtcher, Danish lyric poet

• Ludvig G. Braathen, Norwegian shipping magnate and founder of the Braathens airline

• Ludvig Daae (disambiguation)

• Ludvig Engsund (born 1993), Swedish ice hockey goaltender

• Ludvig Faddeev, Russian theoretical physicist and mathematician

• Ludvig Gade, Director of Royal Danish Ballet 1877–1890

• Ludvig Hammarskiöld, Swedish officer and military historian

• Ludvig Hektoen, American pathologist

• Ludvig Holberg, Danish-Norwegian writer and playwright

• Ludvig Holstein-Holsteinborg, Danish politician

• Ludvig Holstein-Ledreborg, Danish politician

• Ludvig Jansson, Swedish ice hockey player

• Ludvig Mylius-Erichsen, Danish explorer

• Ludvig Nobel, Swedish engineer, businessman, and humanitarian

• Ludvig Schytte, Danish composer, pianist, and teacher

• Ludvig Strigeus, Swedish programmer

• Peter Ludvig Sylow, Norwegian mathematician

• Ludvig Sylow (DBU), Danish football executive