There is certainly a tradition of removing public hair in the Ancient Islamic world.

The Hadith ( oral tradition and law, as opposed to the Holy book of of the Koran) requires a state of 'Fitra', a state of cleanliness which requires trimming of the fingernails, armpit and mustache hair, circumcision, as well as pubic grooming.

The Fitra also stipulates that the pubic area should not be left to grow more than forty days without grooming.

Interestingly, the removal of eyebrows (al-namas) and beard hair is forbidden (Haram).

Methods for hair removal would include Threading- (Fatlah), using thread to remove hairs, Sugaring - a hot paste of sugar and sometimes lemon juice applied to the skin and pulled off, and tweezing, manually pulling out the hairs with tweezers.

Source: 'Nine Parts of Desire' by Geraldine Brooks
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Like, super super duper duper NSFW warning, but this answer about such 'grooming' in the 20th century likely would be of interest for you, courtesy of myself and /u/kieslowskifan.

About a month ago there was a post on r/trippingthroughtime which showed a Medieval bas-relief of a woman shaving her pubic hair from the 12th century. It is currently held in the Museum of Ancient Art of the Castello Forzesco in Milan and is called "Donna Impudica." Sadly, the sources I have found to try and learn more about the topic are either in Italian or require a subscription to gain access to. This does however, provide a very real record of some sort of grooming much before now.