Modern English monkey does not represent a Romance loan-word of Arabian origin and transmitted by Middle Low German but is a vernacular diminutive derived from monk.
The origin of the Mode word monkey, recorded since 1530 in John Palsgrave's English--French dictionary Lesclarcissement della langue francoyse, ranks among the etymological riddles still to be solved. Whereas only a few etymological dictionaries like ODEE (1966) or Hoad (1986) rightly content themselves with the statement "of unknown origin", the great majority, including NED  = OED (1-2), Skeat (1910), Holthausen (1949), Partridge (1966), Klein (1966-67), Barnhart (1988), Cannon (1994) and Terasawa (1997), with varying degrees of uncertainty and dubitation consider monkey to be a MLG loan-word. OED (3) Online now presents the most recent and somewhat elaborated version, drafted in June 2008, which in the end is based on NED and runs as follows:
The immediate etymon of monkey perhaps or presumably is MLG * moneke. The unrecorded appellative can be inferred from the name of a character in the MLG version of Reynard the Fox called Moneke whose name denotes 'monkey' because his father was Martin the Ape. In an earlier Middle French context the name appears c1330 in the form Monnekin ~ Monnequin which probably is a diminutive formation with the suffix MLG -kin, MD -kijn on the basis of MFr monne 'monkey'. MLG *moneke contains the same root and conceivably was introduced into the English language by itinerant German entertainers. As far as MFr monne (1545-1611) is concerned, the word goes back to It monna (1547), (1) whereas ModFr mone (18th cent.) is borrowed from It mona (16th cent.) or from Sp mona (c1400), -o (cf. FEW, XIX, 115-118; DEI, IV, 2492, 2497; DECH, IV, 123-125). It, Sp and Cat mona are generally explained as shortened forms of It maimone, Sp maimon (c1326), Cat maimo (1284) and OOcc maimon (1339) < Ar maymun adj. 'blessed', developed by aphaeresis because the original forms allegedly were reanalysed as being reduplicated (cf. DEI, III, 2321; DECH, III, 771f.; DELCat, V, 373).
Regardless of the phonological and semantic difficulties, which the Romance etymologia remota presents, the common derivation of monkey is hardly tenable for several cogent reasons. Firstly, according to sixteenth-century -spellings such as ModE monkey with /[??]/ < EModE /u/ cannot be derived from an etymon with /o/ like MLG * moneke. Secondly, as MLG Moneke is attested only once the probability that the proper name had such a wide range that it could have been used in deonymic function as a common noun tends toward zero, all the more so since it would have been a hybrid whose French root was not borrowed into MLG. In an unsuccessful attempt to overcome these difficulties Barnhart (1988: 674) alternatively suggests that monkey could have been adopted directly from It monna or Sp mona and represents a diminutive formed with an otherwise unknown suffix -key. Yet there is an element of truth even in this proposal.
Sixteenth- and seventeenth-century spellings such as strongly suggest a different and in addition simpler solution (cf. Dietz 2006: 573). In particular Shakespeare's examples Macbeth 4.2.60, Othello 3.3.408, 4.1.126 provide evidence for the finding that monkey is a vernacular diminutive formation made up of the root monk and the hypocoristic suffix EModE -ie ~ -(e)y, for which see Koziol (1972: [section] 489), Marchand (1969: 298-299), and OED3 s. v. -y suffix (6), -ie. Its semantic motivation is based on the appearance of certain small or medium sized tailed primates. Especially as capuchin monkeys which belong to the family of Cebidae look, as their name implies, like little (Capuchin) friars. Furthermore monkey is semantically motivated by the mediaeval tradition according to which the figure of the ape was mostly used in satiric portrayals of the clergy. …