Recent US usage appears to conflate this proverb with the devil finds work for idle hands to do (see quot. 2001).
The idle bodie and the idle braine is the shoppe [workshop] of the deuill.
[a 1602 W. Perkins Works (1603) 906]
Idle Brains are the Devil's Workhouses.
[1732 T. Fuller Gnomologia no. 3053]
An idle brain is the devil's workshop.
[1855 H.G.Bohn Hand-Book of Proverbs 311]
Steady employment‥ keeps one out of mischief, for truly an idle brain is the devil's workshop.
[1859 S. Smiles Self-Help viii.]
Tell him to be [a] good boy and study hard. An idle brain is the devil's workshop.
[1930 E. D. Biggers Charlie Chan Carries On xxii.]
‘Idle minds are the devil's workshop.’ She lifted the watch‥and stared at it accusingly. ‘Five minutes after eight. Is no one else here?’
[1988 C. G. Hart Design for Murder ix.]
Young people need to learn to work. Their parents must not let them be idle all summer for, as they say, idle hands are the devil's workshop.
[2001 Washington Times 3 Sept. A12]
Related to: idleness; wrong-doers
Bibliography of major proverb collections and works cited from modern editions is available here.