He first trained as a stonemason before studying at the Royal Danish Academy of Fine Arts where he was awarded the grand silver medal in 1856.

He also worked for Johan Daniel Herholdt during the construction of Selchausdal Manor (1857) in Kalundborg, thus receiving insights for the most prominent architects of the day.

[3][4] Klein was particularly fond of the Rosenborg style based on the Dutch Renaissance trends under Christian IV, crediting Bindesbøll for its prominent place in Danish architecture.

From 1866 to 1872, he undertook substantial extensions to Bindesbøll's Lægeforeningens boliger social housing development in the Østerbro District of Copenhagen.

[3][5] [6] Vilhelm Klein is listed in the Danish Culture Canon together with Michael Gottlieb Bindesbøll in connection with the social housing development in Lægeforeningens boliger—Brumleby.