Wallick was a pupil of N. Abildgaard at the Academy in Copenhagen between 1795-1803. In 1803 he left for Rome to study theatre decoration. He there belonged to Thorvalsen´s and the Danish diplomat Herman Schubart´s (1756-1832) circle. Between 1806-09 he studied theatre decoration under Paolo Landriani (1757–1839) at La Scala in Milan and between 1811-13 under Pierre-Luc-Charles Ciceri at the Opera in Paris, the two most important theatredecorators of the period.

Between 1814-45, Wallick was employed at the Royal Theatre in Copenhagen as stage decorator. His sister Frederikke Wallick accompanied Thorvaldsen on his return to Denmark from Italy in 1842. Arnold Wallick´s broher was the famous botanist Nathaniel Wallick (1785-1854 London).