Hendrik Johannes Weissenbruch, also known as Jan Hendrik, was born in The Hague on 19 June 1824, the second son of Johannes Weissenbruch and Johanna Hendrika Zaag. He came from an artistic family. His father Johannes, a chef and restaurateur, painted in his free time and collected art on a small scale. Among Johannes collection were works by Andreas Schelfhout and Bartholomeus van Hove. Johannes cousin Jan (1822–80) was a well-known painter of townscapes. Another cousin Frederik Hendrik (1828–87) was a lithographer, while his younger brother Frederik Johan, his uncle Daniel and his nephew Isaac (1826-1912) were all engravers.
When Jan was sixteen years old he received drawing lessons from Johannes Low. In 1843, he took evening classes taught by Bartholomeus van Hove at the Hague Academy of Art. During the day Weissenbruch worked in Van Hoves studio, together with Johannes Bosboom and Salomon Verveer, helping to make pieces of scenery for the Royal Theatre.