The online OED has an interesting etymology of monkey-business:
colloq. (orig. U.S.).
[< MONKEY n. + BUSINESS n., probably after Bengali bā̃drāmi. Compare modern Sanskrit vānara-karman (< vānara monkey + karman action, work, employment), Hindi vānara-karma.]
Bengali বাঁদর bāndara is “monkey” and বাঁদরামি bāndarāmi is “mischievousness; a monkey-trick; monkeyism”. But it seems strange that monkey-business, a US usage, would be a calque from an Indian language. None of the citations give any clue why this might be.
1858 T. P. THOMPSON Audi Alteram Partem I. lxv. 249 The Native Indian term for the supreme of folly, is ‘monkey business’.
1883 G. W. PECK Peck’s Bad Boy 109 There must be no monkey business going on.
1934 C. DAY LEWIS Hope for Poetry vi. 29 A pandemonium of slogans, national anthems, headlines..manifestos, monkey business.
1972 ‘H. CARMICHAEL’ Naked to Grave vi. 79 Because I’ve seen her talking with one of the neighbours isn’t to say there was any monkey-business between them.
1996 Sugar June 112/2 If you’re up to monkey business, be extra cautiousyou could get caught out.