small cucumber used for pickling, 1660s, from early modern Dutch gurken, augurken (late 16c.) "small pickled cucumber," from East Frisian augurk "cucumber," probably from a Balto-Slavic source (cf. Polish ogórek "cucumber"), possibly ultimately from Medieval Greek angourion "a kind of cucumber," said to be from Persian angarah [Klein, etc.], but OED seems to regard this as unlikely. A Dutch source says the Greek is from a word for "immature" and that the vegetable originated in northern India and came to Eastern Europe via the Byzantine Empire.
The Dutch suffix is perhaps the diminutive -kin, though some regard it as a plural affix, with the Dutch word mistaken for a singular in English. The -h- was added 1800s to preserve the hard "g" pronunciation.