Green’s Dictionary of Slang

(US) a cell, a lock-up.

1911		Truth (Sydney) 19 Mar. 12/3: Them officials in the booby, / They are glad to see them come; / Any change — it’s all the same sir, / When they gets ’em In that drum.
1914		Truth (Melbourne) 21 Feb. 12/6: She gets three months in the Booby.
1930		G. Milburn ‘The Dealer Gets It All’ in Hobo’s Hornbook 150: When old Justice Grimes espied us, and called the constabule, / Who tossed us in the booby, and took away our mule.
1938		F.D. Sharpe Sharpe of the Flying Squad 329: booby or booby hutch : The cell.
1950		Goldin et al. DAUL 31/2: Booby. 1. A jail, usually small and rural.